Thanks for your response, Steve in Austin has been really helpful with my research on this gun that has been in my family for about 40 years when it was given to my father, a physician, as a gift.
I'm not looking to sell it, only have it insured properly and maybe get it restored.
After finding out about the Birmingham proofs I wrote to the curator of the museum there, he sent this information:
Dear Sir
In our view what who have is the end of the company by George Bolton who died in 1806 prior to this being proved. We opened in 1813 and the proof marks were in use in the format shown between 1813 and 1855. J.H. appears to have taken over dads business but still used his name. We are sure its G not C.
Regards
David Evans Curator

He also sent information about George Bolton and his son, J.H., Which I tried to attach unsuccessfully.
If anyone knows more about this manufacturer or where in SC or close by, I could get it restored please let me know.
Thanks,
John K.