Can a sinus infection cause teeth pain in both upper & bottom of right side if face?

Yes surely: Anatomically, sometimes the root apices of maxillary molars and premolars can intrude into the sinus cavity and seasonal allergies, or upper respiratory infection, sinusitis, and the pressure and congestions that comes with these can cause the teeth to ache - when there is nothing wrong with the teeth. You can get referred pain to the lower arch as well.

It's possible: There's only 2 layers of cells between your upper root tips and the inside of your maxillary sinus. If sinus inflamed, can feel like toothache. Can have referred pain to lower teeth, although less common. Sit dow, bend over and put you head between your knees. If pain increases it's sinus, see an ent. If pain doesn't change it's dental, see a dentist.