I've had a strong burning sensation while peeing, and, a yellow puss-like discharge from my penis, what are possible causes of this?

STD. I agree. I would also suggest that if the test results reveal that you do have a std, then all your partners be notified so that they can be tested and treated (if necessary). Again, using a condom and practicing safe sex can almost completely prevent a std.
Probably an STD. You will need to be checked by a doctor to screen you for gonorrhea and chlamydia as soon as possible and then treated. Meanwhile no unprotected sex until you have completed treatment.
Discharge from penis. There are many things that could be causing your symptoms but the most concerning would be that you have been exposed to a sexually transmitted disease. You need to be seen by a health care professional as soon as possible, and until you are seen by a dcotor i would adivse you to stop having sexual relations. If you do not have a regualr doctor an urgent care or health clinic can see you for this.
Gonoohea or a UTI. Yours are the classic symtoms of gonorrhea (gc). Have you had unprotected sex with a partner who may have gc?. Perhahs you have some other kind of urethritis, but, you must get this checked out asap. Good luck.