I completely empathize with you!!!
From day one, my little boy was a "barracuda"... all he did was want to nurse (with quite a bit of enthusiasm) and sleep. When the nurses at the hospital came in they all commented, "he's STILL nursing!?!?" and many insisted on taking him to the nursery so that I could get sleep. I didn't let them because I'd read a lot about establishing milk supply depends on the frequency of nursing sessions, and if he was in the nursery instead of with me, my milk would take longer to come in. He nursed so much that my nipples cracked and bled and I could not nurse on one side it hurt so terribly bad. The lactation consultant made her visit the second day and gave me what saved our nursing relationship: a nipple shield.
His frequency of nursing continued for months... I remember feeling the same was as you. Needing a break! All I am is a milk machine... a breathing pacifier... I felt very used up and needing a "makeover". The worst part was that it was around the clock, even at night nursing was necessary atleast every 2 hours. I made due by sleeping with him throughout the day during those first couple of months. The only thing that I could think was, "It's ok... he's sucking away all my pregnancy weight!" and it really did help! I weighed less 3 months post partum than I did before getting pregnant.
We discovered that our son was allergic to milk, and later soy & egg. He screamed most of the day if he was not nursing or asleep (because of something I ate), and could only sleep if held, sometimes we could trick him after he fell asleep and put him in the swing on low. It took a long time to figure out everything... We couldnt even use vegetable oil for cooking (it's 100% soybean oil) or it would hurt him. Lunch meats had milk products in them. Butter & margarine is made with milk or soy. We made a lot of mistakes for many months trying to figure out what I could and couldn't eat. Our attempts with formula were met with very angry cries, and what he did get down hurt him worse than my milk when containing the allergens.
He didn't want a pacifier either. We spent a lot of time holding it and offering it around 2-3 months and he eventually accepted it if he wasn't hungry around 4 months.
Between the constant screaming, feeling used up, and not being able to eat much of anything that I "enjoyed", I was pretty exhausted and probably a good bit depressed.
I know that's a lot of background information but wanted you to see where my suggestions were coming from...
The first thing that I want to point out is that a lot of women get overwhelmed by the frequency of nursing in the beginning, and begin to supplement, and then their doctors tell them that they do not have enough milk supply to be sufficiently nursing exclusively. So then the mother, trying to do what every mother wants to do, ensure her baby gets enough to eat, ends up going 100% formula. I don't think people really communicate realistically how much and how often babies nurse in the beginning and this is why this cycle happens. There is nothing wrong with formula! However, in my opinion, after those first couple of months nursing is SOOOO much easier to breastfeed! No toting around bottles, no cleaning the bottles, no formula runs because you ran out, no worrying about wasting the formula because you're not supposed to keep it but for X amount of time once it's mixed... I'm sure you're already aware of all these things. The real kicker for me is the diapers too... Wow when my son started eating solids it was a turn for the worst in the stink department, I really miss when he didn't smell so bad! lol. So don't think that your baby is nursing too much at this point. She's only 4 weeks old, and she's trying to establish your milk supply. They go through SO many growth spurts very close together in the first few months, and EACH time they're going to nurse like there is no tomorrow. Take into consideration too when others try to tell you that she shouldn't be eating that much/often: some babies have higher metabolisms. Not all babies are the same, as we know, and this is no exception. I'd suspected that my son ate as frequently as he did because of hurting (soothing milk effects initially then the pain of allergens, seek soothing milk again, etc cycle) but later when we started on solids we discovered he was just a voracious eater. At 8 months he ate a plate of speghetti equivalent to what my husband ate and wanted more. He is still this way at 14months, and is thin as a rail though was FAT FAT FAT at 2-10 months (95th percentile weight)! If your baby is thriving through the 2 week and the 1 month check up at the doctor I don't think that your milk supply due to reduction surgery is a problem. I'm not a doctor though either! But the proof is in the baby and if the doctor didn't say... "she's underweight... dehydrated... not thriving..." etc, then I think you're doing a FANTASTIC job as a demanded, yet-to-be-appreciated "milk machine" :). Know that women who have not had that extra complication of worrying about a real reason they may not be producing enough milk, still worry about producing enough milk. You can't SEE or MEASURE it, it makes it hard to feel confidant when the baby is nursing 24/7. It doesn't help if you have friends asking how much your baby eats either, if they formula fed, haha :).
So I just wanted to tell you to hang in there, give it to 2 months, just 4 more weeks, if you can. I think you'll see a nice regulation in frequency that will give you more You Time. You chose to breast feed because you believe it to be a good thing, and I think you'll find that it's well worth it when your finish breast feeding relationship. My son still has not had a single cold or ear infection, and I'm sure it could be luck but perhaps it's due to all those good immunities he sucked away from me! If someone had told me that I would have a baby stuck to my breast for as long as I did before I started I probably would have began with formula off the bat, especially after knowing that I would have to limit my diet to no bread, chocolate, cheese... which meant NONE of my favorite foods. But no one told us that we'd be milk machines and here we are.
And I just re-read your post and found a really big sentence that I initially missed: "I honestly didn't want to breastfeed exclusively, but it appears I don't have a choice."
You certainly do! It's harder to manage both but what the other ladies posted about having someone else feed the bottle is great advice. With my son I felt the need to teach him to drink from a bottle in case I wasn't around, so we pumped and gave him the bottle. At first you had to bounce and walk him while feeding him, quite a sight and difficult to do with two hands. It takes a lot of patience from the feeder. I think it took 3 attempts of this circus act before he would drink more than a couple swallows.
You didn't say that they did, but if your breasts hurt, think about getting a nipple shield. I have read a lot of disapproval about them, regarding nipple confusion and such, but if it makes the difference between you being able to nurse or giving formula, then do it. At 2 1/2 months I took the shield away and had my son nurse without it. At first he was a little confused because it's not as easy to latch on without it, but it didnt take long for him to figure it out. They like their breastmilk :). Get atleast 2 of them, because they manage to disappear sometimes.
And you also didn't mention how your little girl acts during the times she's not nursing/sleeping... but keep your eyes open for possible allergic reactions to your milk. I wish someone had told me to consider it sooner!
Sorry the post is so long! I wish I could help and all I have are words. Let us know what happens in the next few weeks :).