My ENT doc thinks that my left tonsil must be taken out because of an infection or a stone, but I have no fever or difficulty swallowing, just pain and sore throat pain behind my nose and left cheek and ear. Is that normal?

Get a second opinion. Get a second opinion from another ent. If you develop frequent infection then removal of tonsils may be wise.
Which? Certainly not normal to have persistent pain and sore throat and pain behind nose and in cheek and ear. It is normal for an ENT doctor to want to remove a tonsil which he believes is not functional and is creating more problems than benefits. If you still have questions, ask for another independent opinion.