I found out my preemie had reflux at 2 months, (which would have been right around her due date.) A few weeks later I found out that she has a protein allergy, for not only dairy - but soy products as well. So it was just blow after blow for my wanting to nurse. I watched every thing I put in my body to make sure I wasn't getting anything that would worsen her reflux. But because dairy was such a big part of my diet, my supply slowly started to diminish. Eventually I barely had anything left at around 7 months.
Reflux sucks. DD was put on Reglan and Zantac and if I didn't have any stored breastmilk, (and I was working) she would be given Nutramigen. I digress.... my whole point of rambling comes down to this. Rice Cereal. I was VERY hesitant to put a thickener in her bottles because the pediatrician didn't recommend it. It wasn't until DD was visiting my parents at around 4/5 months and my mom decided to try it without asking. (She had been encouraging me to do this, but because of the Pediatrician, I kept saying no.) I was astounded at the difference it made. I immediately took her off of the drugs, and put a tsp. of rice cereal per 2 ounces in her bottle every time. I kid you not, she didn't spit up again (AT ALL) until she was about 10 months and I was attempting soy formula to see if she was ready yet. Obviously she wasn't and she spit up immediately, but that was more related to her protein allergy rather then her reflux.
Some cases of reflux are much more severe then my daughter's. So I would pump my milk when I could, put it in the bottle, add the rice cereal and it just worked like a charm. She still got her BM and I got my sanity back (and my clothes!) I'm a huge fan of breastfeeding - so I encourage you to try to continue as long as you can. Try not to stress, and always be open to other options! Good luck and I hope that you get this figured out!