After you get a chlamydia shot can you still pass it on?

Shot ???? I know of no "SHOT" that is among the many treatments recommended to treat chlamydia. Are you sure it was for chlamydia and not gonorrhea ? Either way no treatment is effective immediately and how long you remain contagious would depend on the real diagnosis and treatment. If you must be sexually active use a condom at least until you clarify the issue.
Usually not. Chlamydia infections are often treated by oral antibiotics. If a patient got a shot of antibiotics to get rid of a chlamydia infection, then he is likely cured, after a few days. Cure rates are never 100%, so the patient may want to be rechecked by his doctor. Also, every person the patient had contagious contact with would have to be treated so that the patient doesn't catch it back again.