Hi, Kim. Every answer that you have gotten could be right. Cracks on the paint on your walls can originate from everything from incompatible paint to your foundation settling. It's about impossible to tell without seeing your house, it's structure, location, surrounding geography and many, many other factors.
The peeling paint is a good clue that it is either a paint or moisture problem. It would help to know how old your house is, how long you have owned it, what painting you have done since you moved it, etc. Even with that,there is a good chance that the problem cannot be diagnosed on the forum. You may hear some other answers here as well. They could be right. The best way to get good, realistic info though is to ask the oldest, crotchitiest painter you can find to quote you on painting a couple of rooms. Then let him do the work. At least you will see what he did so you can do more roons the same way.