Penis has a ring pierced thru tip. Has been 4 weeks. Had sex. Irritated, swollen, oozing, pain. Two questions: is it possible I have a tear? Also, what antibiotic treatment (already used amoxicillian) should be used

Sounds. Sounds like you have an infection around the foreign body (ring) and may have to be removed for infection to clear. You should see a urologist before infection spreads to the rest of the penis.
1.. 1. Did a physician or other health provider prescribe the Amoxicillin and if so, did you take the medication for the complete course and as directed? If evaluated, was the irritated, oozing part of your penis tested for what type of infection it was? 2 when you were sexually active did you use protection such as a condom? 3. Is the ring still in place and what metal is it made of?