Did your SO know you were pregnant when he purchased the tickets? Sounds like he didn't think ahead about there being a baby in the picture. I'm shocked that he just told you recently and the trip is in a week. I'd be having some serious conversations with him about communication.
Your baby will not remember that you left - so it's nothing he's going to hold against you for the rest of his life! He is attached to you, of course, but he doesn't have the emotional development yet to really feel "love" as we know it. So he won't stop loving you. He will take some time to get used to you when you come back and he may be temporarily attached to the person who is his primary caretaker while you are away. That person may have a couple of rough days when you first leave, and you may have a couple when you return. But lots of women have done this, and your pediatrician has confirmed that your child will be fine.
No baby 7 months old will take a zippy cup or drink through a straw. So don't even try those yet! The baby will take a bottle from someone else - maybe not from you, but he will not starve. The thing to do now is to pump breast milk and have someone else give him the bottle. That's kind of a nice thing anyway because then he can be comforted by a second person and learn that others provide sustenance.
Yes, you would be engorged if you tried to go a week with no breast feeding. So you either decide you are done with breastfeeding and want to wean the baby (which it doesn't sound like you do) or you pump and dump the breast milk.
But it sounds like you are already under stress from other things - you say "I've got so many things worrying me and on top of it…" you'll be miserable on vacation. So there are other factors besides a vacation. You may have a ton of stuff on your plate, or you may have anxiety -- so those things need to be dealt with.
Is being away from a baby difficult? Yes. Do new moms need a break sometimes? Absolutely. You are not just a mother - you are a woman, an adult, a partner in a relationship. Only you can decide if some alone time for yourself with no one wanting a piece of you would actually be a wonderful thing - taking a walk by yourself, sleeping late, perhaps even having a couple of cocktails (since you will be dumping your breast milk) - or spending some alone time with your SO after all this focus on a new baby might be lovely and restorative, letting you reconnect. Is this a good gift to your relationship? Your child is entitled to 2 parents who are happy and secure and connected.
Otherwise, if the tickets can't be delayed or transferred, you can just take the financial loss and stay home where you will not have to deal with this question. And your SO needs a good talking to for not discussing this with you until recently so there would be more time to prepare emotionally.
So ask yourself if you will regret not taking this trip - at some point you do have to separate from your child. They need to build independence at some point. Would a break from the problems in your life be good for you emotionally, and would a change of scene be beneficial? Is this the time?