Dear Candidate

See as per your Marks-349 it is difficult to get a Government Medical Seat even if you have a state quota and another quota if applicable. You should have maintained a score above 550 to be on the safer side.

You cannot get into any medical college with this mark.

Yes you can apply at St. John's.

At this stage, I will suggest you must use this link to get a fair idea about the colleges both Private and Government you can get as per the score you have received and then plan accordingly.

https://medicine.careers360.com/neet-college-predictor