How do I check my work is worthy?
Regarding the Ph.D. part of the question, only a school can grant a Ph.D., and no school will grant you a degree if you are not enrolled as a Ph.D. student.  Your best bet is probably to contact the mathematics department at a nearby research university and ask if a faculty member would be willing to look at your work.  If you have really been doing original research on your own, then you can probably be admitted as a student and begin working toward a degree.

Regarding the journal part of the question, most journals do not charge fees to authors (they make their money from subscription fees).  Most journals have web sites that explain the format and process for submitting a paper.  See http://en.wikipedia.org/wiki/Academic_publishing#Publishing_process for a description of how this works.