Hi!
You've gotten some great information above, just going to add along.
I knew Gwyneth had a milk allergy/ intolerance very early, around 3 weeks old as she became extremely fussy, was congested all the time, had painful gas and bowel movements and eventually had mucous and blood in her stool. I cut all dairy and soy immediately. My LC said the same thing about hidden dairy being ok, and it is widely held in the medical community that such a tiny amount of the offending food, becoming even tinier and going through your BM should have no impact on your child. That was not the case with us at all. Gwynnie was so incredibly sensitive to any tiny little bit of an unsafe food. We ended up having to deal with many many food intolerances, but there are lots of good substitutes and a little adjusting will go a long way.
I too did't cook from scratch all the time. Well, that changed quickly, lol! It is amazing where milk is hidden, as vikki said - deli meats, hot dogs, soups, dairy free creamers! Seemed it was everywhere. Takes a little bit of doing, but you will become very familiar with labels.
We often would cook a huge roast, and have it for dinner, then I would slice it for me for lunches and snacks. Fresh fruits and veggies, pop corn, chips and salsa, almond or coconut ice cream, there are some margarines that are corn based that can be subbed for butter. You can make your own bread and cakes. The biggie for me was cheese, I loved cheese and there really wasn't a decent substitute. I ended up in such a strict ED though that I couldn't have most of these things for a while.
I saw an improvement right away, within a couple of days she was a happier baby, sleeping better. It can take 2 weeks to get the proteins out of your system, and then another 2 weeks to get out of your LOs though. It took us a LONG time to get to a safe baseline where she was completely fine however, as we found through trial and error we were dealing with many food allergies/ intolerances. Milk was the big one though, so ditching that made such a big difference.
As far as introducing formula in the future. If you notice an improvement cutting the dairy and soy, then I would assume an intolerance and start off with hypoallergenic formula, like alimentum or nutramigen. Most babies can tolerate those, some can't ( mine could not) then it would be to an elemental formula like neonate or elecare. Start slowly, an ounce or so a day to see for any reactions, and go from there.
Make sure to take a calcium supplement, and hang in there!! Huge huge hugs to you and your sweet baby, it can be overwhelming and frustrating nailing down the issue, but once you start to see an improvement it makes it so much better.