I am sorry to hear you are worried about Bear. My name is Rebecca. I am a veterinarian and will do my best to help.
Is he eating well, and normal apart from the sneezing?
When he sneezes, is there any blood or discharge coming from his nose?
He may have something in his nose (I once saw a cat sneeze violently for 2 weeks, until he sneezed out a long piece of grass!) but then you might see drops of blood when he sneezes.
He may have a viral infection, or allergies. You could try children's nose drops such as Little Noses, 1 drop in each nostril once to twice daily. If he is eating normally and not sneezing blood, that might help.
Is there any eye discharge at all? If so, you could try Terramycine eye ointment which is available in most states without a prescription.
Let me know what else I can answer.