Sounds like my story. I didn't produce enough milk so we had to use formula. At about 6 weeks I noticed the same thing gas and irritability. At about 2 months I started to notice mucus in her poop (never any blood). Under the referral of our Ped. we went to a GI Dr who did a biopsy and determined an allergy to milk. This procedure sounds extreme but in really wasn't. The GI Dr didn't recommend Soy because the protein is about the same size as dairy and most babies still have a hard time digesting it. He put her on an Amino Acid based formula called Neocate. It's expensive but here in CO our insurance is legislatively required to cover the formula.
She is now 10 months and is still on Neocate. No problems since then. She will stay on it for her first year. We'll then try here on regular formula for year two. 90% of kids outgrow the allergy in the first year. There are a few things I give her that have dairy in them (crackers) and she doesn't have any problem with them so I think she has probably outgrown it.
I would definitely consult your Ped. Left untreated it will usually cause blood in their stool, which is usually when parents first notice a problem.
Let me know if you need help with dairy free finger food! Good luck.