Yes there are nail magazines. I have been able to find at least one that specialize in the Nail care industry. It is named Nails Magazine. Also there is Nails Art and Nails International.
Simply typing in nail magazines in a search engine will give you a lot more choices than just these three.
Yes, I know of two of there, but there are probably more. There is 'Cuticle Quarterly', and 'Fancy Nails'. If you ask your nail person they may be able to tell you about others.