You received oral sex, I assume?
The risks for that are syphilis, gonorrhea, chlamydia, and genital herpes type 1.
The risks don't change because the cyst burst. That may become infected by normal mouth bacteria, but it won't be an STI.
If you gave oral sex, the risks are oral gonorrhea, chlamydia and syphilis.
You can test for gonorrhea and chlamydia both orally and genitally at 5 days. Make sure to get an oral swab and a genital test (either urine or a genital swab).
You can get a syphilis test at 6 weeks.
If you don't already have oral hsv1, you can get a type specific IgG herpes blood test at 6 weeks, or get a sore cultured if you see one sooner. If you don't see a sore, you can skip this test. It's often run with a type 2 test, and there are false positives on the type 2 test.