Had sex may 21st. period due may 24th, im 6 days late, got a faint positive on an at home test. may 30th negative blood work with progesterone level 7.4. could antibiotics delay a period? whats going on?

If the "negative blood work May 30th" included another negative pregnancy test, pregnancy is unlikely, however, delays in ovulation will delay the next period and "sex on May 21" could have occurred while ovulating, so a serum HCG test, which can detect low levels of pregnancy hormone. If the test is positive, see your GYN physician for guidance and other testing.