I have a sinus infection (viral, I think) and I am on antibotics. I have shooting teeth and jaw pain at random times. What can I do to relieve this pain?

MD first, then DDS. Viral sinus infections will not be helped with antibiotics. But it might help reduce some swelling associated with the infection. I'd recommend considering consulting with your physician about some sinus drying agents like pseudophed which can also help reduce some of the inflammation which can send pain signals to the teeth. If that doesn't work, then time to see the dentist.
Viral infection. You say you have a viral infection. If this is a definite diagnosis, antibiotics will not help cure the infection. Visit your primary care physician or an ENT doctor for the sinus problem and visit your dentist to evaluate your intermittent teeth pain.