Congrats on your new baby!
Well, the only way to be sure is to trial an elmination diet and see if there's any difference when you reintroduce foods. Soem mothers find there seems to be a connection between certain foods and baby's behaviour. and some babies have serious reactions to certain things, though I think you'd realise if that were the case. I think often though it is just a coincidence as they change so frequently in the early days - sleeping well one day and not at all the next!
Lactose intolerence is extremely rare in babies since lactose is also the sugar in breastmilk - I'm not sure that cutting back dairy would change the lactose content of your milk Some babies do react to the proteins in milk, however.
If she has a cold that would explain all sorts of different sleeping/settling/feeding behaviour. Hope she's well soon!