I have done B.Com (management Hons.), MA in Journalism and mass communication and B.Ed in arts. Can I apply TGT or PGT?

Yes, you are eligible for TGT (especially in Social Science or Commerce, depending on your subjects in B.Ed and B.Com).

You are not eligible for PGT unless you get a post-graduate degree in the subject you want to teach (e.g., M.Com for PGT Commerce).