If you get a seat in a self-financing medical college through state quota in the 1st round, you can still participate in further 2nd and 3rd rounds of counselling, but this depends on the rules of the respective state counselling and MCC guidelines.

Regarding shifting to All India Quota, if a seat is allotted to you in the 3rd round of state quota counselling, you cannot opt for AIQ in the same academic year because AIQ counselling is conducted before or alongside state quota rounds, and once a seat is confirmed under state quota, you are generally locked into that seat.