Tom is sitting beside John. Can we use "next to" here?
The bank is next to the drugstore. Can "beside" used here?
Tom is sitting beside Joe is
Cambridge Dictionaries Online - Cambridge University Press
except and besides are chalk and cheese.
Your sentences are correct. And you can also say "The bank is beside the drug store" or "Tom is sitting next to John."
Some may prefer one preposition over the other, but the meaning stays the same and both are grammatically correct. (At least in standard American English.)
-Lola (native American English speaker, ESL teacher)