I have a swollen knuckle and pain there. Could this be gout?

Possibly. Did you injure your finger? Have you had gout before? Is it hot and red? Do you have any rashes on your skin? Do you have diarrhea? There are so many things that it could be gout is only one possibility!
Possibly. Gout, arthritis, trauma, certain diseases of the skin like psoriasis can also cause it. If conservative home remedies don't offer some relif you should see your dr. Sooner than later!