Yes, David, I think it is very likely that you are having seizures. From what you describe they are called "Focal Motor seizures with Jacksonian March" . This means that you start to have a very localized seizure in your hand, but then it "marches" to involve the whole side of your body and sometimes the entire body. The other episode you are having sound like brief Partial (complex - maybe) Seizures. You need an evaluation of this immediately. If this happens while your are driving or swimming it could be disastrous for you and possibly for others.
They will need to do a brainwave tracing called an EEG and probably will do a head scan also to rule out something more serious like a problem in the brain. Do not put this off. Tell your family and get evaluated as soon as possible.
This is most likely not a serious thing like a brain tumor, but that has to be ruled out. My sister began to have identical seizures when she was 19. Hers are very easy to control.
Good luck, and please come back and tell us what they find. If it is a simple partial or focal motor seizure, it shouldn't affect your life much.