Silence, I'm glad you have had good advice from your GP this time. It sounds like breastfeeding is totally possible for you, and will be the best thing for your baby.
I breastfed DS1 for ages (think years rather than months!), despite his mulitiple food allergies. It isn't easy living on a restricted diet, but I was (and am) more than willing to do it. In any case, it truned out to be very good practice for cooking and meal-planning when DS got bigger and started to eat the family food.
DS is now 5, nearly 6 year old and has grown out of some of his allergies. He is having baked egg and milk carefully reintroduced under care of specialist - I never thought we would get to this stage, but we have! He is still allergic to a lot of things, but life is getting much easier now.
I recommend keeping a food diary of what you eat, so that if your baby does react you will have some clue about what might have caused this.
Also, you really do need to see a good specialist. If you call the Anaphylaxis Campaign, they can direct you to a website with a list of good paediatric allergists who have proper clinics and good resources. You can then ask your GP to refer you.
(Until recently, we saw a local paediatrician who has an interest in allergies. She was lovely, and I have no complaintts about her at all, but she was not able to provide the same level of care as a big clinic. Her last letter said something like "It seems your DS is not growing out of any of his allergies at the moment, so I will see him again when he is six". For the last 8 months, we have been travelling sixty miles to the nearest clinic on the Anaphylaxis Campaign list, and in that time DS has had more blood and skin prick tests, passed a peanut challenge, and started introducing baked egg and milk. Wahey!)
Hope all goes well with your little one, and I am so pleased for you that you are able to carry on breastfeeding. Breastmilk is 70 calories a tablespoon, is a complete and balanced food designed for human babies, and is stuffed full of antibodies and other goodies that can't be replicated in formula. When DS1 was tiny, and I worried so much about not being able to feed him a balanced diet, it was extremely comforting to know that he was getting so much nutrition from breastmilk, and that I could carry on for as long as we needed to.