Would I be able to have strep or tonsillitis only on one side of the throat?

Yes. The bacteria is likely all over your throat but you may only have one tonsil that has significant swelling. However, if one side is markedly swollen to the point that it is causing the uvula to be pulled to one side that could be a serious condition called a peri-tonsilar abscess. That can impact the airway and merits emergency care.