Is it normal to get ear pain and tinnitis when you push hard against the masseter? can this last for weeks? can one side cause problems for both ears?

Yes: Pushing the masseter muscle can hurt the ear and also close the canal. It can cause symptoms of TMJ disease, especially if there is any problems in the canal. If the canal is closed you may hear abnormal sounds or sounds that you didn't notice. It is often hard to localize the side these sounds come from. Inner ear problems can cause similar symptoms. See ENT doc.

No, see ENT Dr: No, should not get pain or tinnitus, definitely not lasting for weeks and not transmitting to both sides. Should see an ENT dr for evaluation.