Experiencing dizziness and lightheadedness but no ear pain. Could this still be an ear or sinus infection causing it?

Yes and other things. The symptoms you list are shared in common with a multitude of illnesses. This could be the early stages of a viral illness, blood pressure issues, blood sugar issues, etc. If you have a recurrent pattern of ear or sinus issues, this may be an early sign, but it is to non-specific to be the only choices.