OP, to diagnose an intolerance you really need a lot more to go with. Your bub may have just not coped well with the first formula you tried perhaps? Some are well known to cause digestive problems, so can be trial and error.
The sleep & feeding you have described is completely normal for 3wks too. My DS2 is 13wks and still can feed every 2-3hrs over night. I think she just spoilt you by giving some longer blocks initially! My DS2 is a very cuddly baby too and will sleep all day in my arms, but not so well in his bassinet yet.
I know the sleep deprivation sucks, it's the worst part of being a new Mum. But as PP have said, you WILL get through it. Don't put too much pressure on yourself or your DD at such a young age. It's hard, but this is all completely normal and part of becoming a parent. Sleep is one of those things we sadly lose in the early months!