Lots of concerns here, and that's okay. It shows you care.
Have you been drinking milk at all while you've been nursing? If he didn't have a reaction then, he probably won't now. Milk proteins pass into breastmilk - if you've been drinking it, he's been getting it. If you haven't had milk at all (I mean AT ALL - sour cream? Cheese? Anything?), you will still know he's having a reaction if and when you decide to introduce cow's milk products. A milk protien allergy will most likely present as diarrhea, and probably a full-body rash to go with it. I had to drop dairy entirely in my own diet until my oldest was six months - she was nursing, and allergic. She outgrew it, thankfully. It seems like your son is getting cheese, though, so if not reacting to that, then milk is most likely going to be fine. (I'm not an allergist, so I won't say it's definately going to be fine, but I'd bet that your chances of an allergy to the same type of milk the cheese is coming from, at this point are pretty slim.)
We are big milk drinkers here. We buy hormone-free milk. We are lucky enough that our local grocery store (HEB) only buys their store-brand dairy from hormone-free dairies. I understand the concern of milk with hormones - I'd probably seek out hormone-free, even if it wasn't so easy for us to find.
As for iron, if you are terribly concerned about it, try introducing Cheerios. They are iron-fortified, and they are just fun for little ones to eat.
My husband and oldest daughter both have texture aversions to vegetables, but we've discovered the joy of V-8 Fusion. True, juice is a best-in-moderation item, but when the kids do drink juice, we make it as worthwhile as possible. Also, Apple and Eve makes Fruitables juice boxes, which is also a combination of fruit and vegetable juice, just in a more convenient box. My kids approve of every flavor we've tried so far.
As for dehydration, once he's got the hang of using them, leave out a sippy of water where he can find it (we always have cups or sports bottles in the same place for our kids, so they know where it is). He knows when he's thirsty - trust him to take care of himself this way.
Hang in there, lady. You seem like a good mom.