Not sure i understand your question about the proton NMR, but having had a quick glimpse at the structure of paracetamol, it should have 5 distinct peaks.
Forgive me if this is too basic for you. There are 5 separate proton environments in the structure - the methyl group as you point out, the OH proton, the NH proton and then the 4 protons on the the phenol ring. These last 4 protons will only give 2 peaks.
The methyl group should be a large singlet because the nearest proton is the NH proton, and is unlikely to have a splitting effect. The height of the peak is unimportant - its the peak integral you're after, which should be 3, 1, 1, 2 and 2, not in that order.
The OH proton peak should (i think) be a triplet as its close to two other hydrogens, and the two phenyl peaks should be 2 multiplets, possibly doublets of doublets. Although if your NMR spectrum is low resolution the splitting patterns may not appear anyway. The coupling constants would allow you to further confirm the structure.