My dentist seems to think my bruxism is what is causing my teeth to hurt so badly that I can only eat on one side, do you think it is possible?

Yes. Bruxism can cause serious pain in your teeth as well as jaw. It can also cause headaches. Talk to your dentist about treatment with an occlusal guard.
Very possible. Your Dentist, an Orthodontist, or an Oral Surgeon can construct an occlusal orthotic, a bruxism mouth guard, for you to wear. This should reduce your tooth pain while protecting your teeth from wear. Then the cause of your bruxism should be determined. If your bite is off, tooth realignment (braces, not Invisalign) may be required.
It is possible. Bruxism is not a dangerous problem. However, it can cause permanent damage to the teeth, severe toothache and uncomfortable jaw pain. See dentists who have more experience in evaluating bruxism.
Sounds reasonable . Given he has evaluated you clinically and subjectively. I would take his advice - his intention is to help you and save your dentition and associated structures. Hope this helps.