CMPI and lactose intolerance are two different things. Sorry to jump in on this thread, I technically don't qualify to be here as I have a 15mo but just wanted to give you ladies some support. My eldest DS us now 6 to but was a horrendous sleeper until he was 2yo and since the age of 4yrs he has slept 12hrs+. This is without sleep training and just being responsive to any wakings. Fast forward to DS2.... I thought I would be due a half decent sleeper, but no, I got one who was WORSE!!!! Until he was 11mo he was waking every 1 - 3 hours, I didn't sleep train but had some 'rules' from the age of 4mo. This consisted of - no co sleeping, no picking up once put to bed, no lights on, no talking, no nappy change unless soiled. Stopped night feed at 10mo (breastfed). When he woke I would pat his bum until he dropped back off, this could be instant or take 1.5hrs+, but I would still not pick him up no matter how long it would take. I stuck to this through the months of waking every hour due to teething, boy it was hard, especially with looking after my other son. Now at 15mo I can put him to bed and walk out and he will chatter away for 10 mins then fall asleep. He still has rubbish nights, which is waking twice usually (so knowing how to self soothing doesn't mean sttn.....!) But by sticking to the 'rules' he knows to expect nothing other than a quick bum pat when he wakes. Each night is different, night before last he woke 4 times, last night he was asleep by 7pm and I didn't hear a peep until 5.30am.
What I'm trying to say is that what you are going through is normal. Some kids get the whole sleep thing straight away, some it takes years. Personally I saw big improvements with both my boys after 12mo. I know that seems far off now but it goes very quickly and you will get through it. I know as I have been there with my eldest and he is now an amazing sleeper and loves his bed. You don't have to do anything to 'fix' it, they will get there. Yes, there are things you can do to encourage them, like the rules we stick to. But never once have I not responded to my boys or let them cry alone.
I recommend a few websites - Sarah ockwell-smith, evolutionary parenting and Kelly mom (the night time parenting section). These are what got me through the worst times and helped me realise things were hard but normal and they would get better. That and stolensleep.com for some light relief! Hang in there girls! 