Treated chlamydia, had symptoms again, results came back that there were traces of it left, treated again. now burning w peeing, & itching/irritation?

Yeast infection?: It is great that you followed up and found out the infection was not gone so could get further treatment. With vaginal itching and burning now, you may have a yeast infection from the antibiotic. Try an over the counter medicine for this, there are several that treat candidal infections. Get seen if you are no better in a 3 days or if you get worse. Avoid fragrances in soaps & detergents, too.

Go back again: Just like you did last time, it would be a good idea to go back and see you doctor. Your symptoms could mean that you were not completely cured, you have been reinfected, or that you have another process going on entirely (urinary tract infection, yeast infection, etc). A doctor visit will help clear that up.

Hard to know: This could be a reinfection, but it could also be a yeast infection. These can be common after taking antibiotics. It would be best for you to be seen by a doctor for diagnosis. Best of luck!