My son is very sensitive to cow's milk proteins and was 22 months old before he could comfortably drink small amounts of milk. I never pushed it on him because as long as he's eating other foods that have the same vitamins and minerals that milk has, I know he's fine. If he wants to drink milk, that's fine, but I wouldn't push it. Remember that we are the only animals that drink the milk of another animal and believe it or not, most kids (and a lot of adults as well) are sensitive if not intolerant to the proteins in cow's milk. If it's the milk you want him to drink, try Lactaid (lactose-free), soy milk, rice milk, or some other variation and see if it helps with the fussiness. If not, it could very well be teething or a small cold or allergies.
As for the bottle, I don't feel right offering much advice because my son just turned 2 and still has his water bottle in his crib for naps and bedtime. I agree with the other mom who suggested putting what he likes in the sippy cup to get him used to the difference from the bottle. If you want to eliminate the bottle completely, you may have to take it away and not let him ever see it again. It's a really personal choice, but whatever you decide, stick with it. Good luck :)