Bit tragic 
.
Fleur they don't really diagnose. Basically HV told me to go to GP as something obviously wrong - she saw a lot of the screaming. Got given gaviscon which made her throw up. I asked GP and HVs at bfing group if I should consider stopping dairy and they all said no, v unlikely yadda yadda. Eventually said to HV and she said she'd phone dietician who called me and said actually with elder child's problem, was very likely and yes cut it out. At same time GP gave me ranitidine for reflux. Within a couple of weeks, massive improvement. However she also hit the 8 week mark when they do start growing out of colic etc and was on ranitidine so was hard to see what made the difference. So after about 3 months I drank some milk just to see what would happen and she puked and had a million dirty nappies and was v unsettled. I recently stopped the ranitidine and she seems fine with that.
Definitions seem to differ depending on who you talk to but my dietician explained it thus (sorry for the length):
There is CMPA (cow's milk protein allergy) and lactose intolerance. Lactose intolerance is extremely rare in babies and children other than temporary cases which result from bad tummy bugs. If baby is lactose intolerant, their body lacks a particular enzyme which breaks down lactose. In this case, they would also be intolerant to breastmilk.
CMPA is pretty common - more so in ff babies. Most children grow out of it. Symptoms can be like typical allergy symptoms - rashes, eczema, anaphylaxis, immediate vomiting; or digestive and delayed - cramps, diarrhoea, blood in stools and various others. I think she said a blood test would only give results for immediate symptoms so if your child doesn't have those, it wouldn't show up. I believe they can test a stool if it is fresh but you can imagine the logistics of this - so it isn't done. Diagnosis is basically done by process of: cut out allergen, see if there is improvement, reintroduce allergen, see if there are symptoms. The dairy will take a couple of weeks to leave your system and then a couple more to leave S's system so you would expect to see improvement around the 3/4 week mark.
Sorry if that is really long-winded or disjointed - baby not settling and tit hurts!
Basically if you think stopping dairy has had a positive effect, I would ask HV to refer you to dietician. Write down his patterns of behaviour now and keep a diary. Also, some babies are allergic to other things e.g. soy, wheat, eggs etc so it can be a bit of a minefield but tbh I'm not obsessive about it. Stopping the screaming was good enough for me!