Just wanted to hop on and offer you lots of ((((hugs)))). I know how frustrating it can be and it's awful seeing your LO in pain and not knowing exactly what is going on.
I echo cutting out soy and dairy right away (even the hidden soy and dairy - there are lots of tricky names for dairy, like casein, whey, etc - there should be a sticky on this board that tells you all the names if you aren't familiar w/them). And as others said - no, I wouldn't eat anything that was made in a factory that also processes the food you are eliminating.
I went on a very hard core elimination diet (am still on it actually, have added back a few foods since getting DD's allergy results) BUT I did it because I myself had tons of allergies until I was about 2 years old. So i cut out everything, and I mean everything except 5 baseline foods to get immediate results. It's difficult to do - but I found that nothing was giving her relief. Come to find out that she has multiple allergies. Very extreme, but some mama's finally go that path. Also - some BF'ing mothers I know cut out the top 8 allergens - wheat, soy, dairy, eggs, tree nuts, peanuts, shellfish, fish and I'm blanking on the last one. I would suggest the wheat, soy and dairy right away if you can - and the first week is the hardest, then it gets easier. I had some headaches as I was "detoxing". As Deb said - it actually becomes pretty great because you cook from scratch. Just be careful and take a calcium suppliment (there are hypoallergenic ones) and make sure that's introduced as a "food" challenge.
More ((hugs)) and good luck. If you have any questions or just want to vent, let me know - I have been doing this for almost 8 months (with GREAT success, but it was a long road) and I know how hard it can be when all you want is your baby to feel good and for everyone to get some sleep!!
Good luck!