If you suspect a dairy or other intolerance pls go to your gp and ask for a referral to gastric paediatrician asap. You can get formula specifically for this. Plus other meds to help with any potential reflux etc.
This was our experience with dd who was a poor feeder, poor weight gain, didn't settle, screamed a lot as if in pain, explosive lose nappies and really poor sleep. She suffered for 3 months but all of this was fixed with nutramigen (formula for dairy intolerant babies) and omeprazol (reflux meds).
We got nowhere with gp or health visitors who just don't have the level of expertise to really understand food intolerances/allergies, so went private to get the much-needs help that sorted all our problems out immediately.
Also on the advice of the gastric paediatrician, we started weaning at 4 months - just a little baby rice mixed with formula once day for a week or two. Then we increased this to twice a day for a couple of weeks. Eventually establishing 3 'meals' per day of baby rice with formula. Plus bottles of milk throughout the day too. We went slowly and this took maybe 6 weeks. Then we introduced real food - puréed sweet potato was a favourite and we also tried apple and carrot - once per day for a week or two, then twice a day, then 3 times a day.
I never hesitated to wean early despite the so called expert advice to wait till 6 months - but then we had medical recommendation to do so. DD is almost 2 now and a great eater, healthy weight and bundled of energy.
I wish you loads of luck. And just know that things get easier 
