Do I publish a paper independently or ask a professor to mentor me?
First, you should assure yourself, and then again, that the work is correct by the standards of your field. It is this point that requires insight into your topic. You know best by yourself whether you need a mentor or not.

Second, you need to 'sell' your work. This point does not require expertise in your particular niche, but it can benefit from knowledge of people in your discipline. This includes aspects such as Academic English, Writing an Abstract, Writing an Introduction, and so on. Maybe there are some trustworthy (!) persons in your discipline that could proofread it for you?