With 339 marks and an All India Rank of 516,000 in the General category , it will be difficult to secure an MBBS seat in government medical colleges in Tamil Nadu or Pondicherry through the All India Quota (AIQ) as the cut-offs for the general category tend to be significantly higher.

However, you might have a chance at:

1. Private medical colleges in Tamil Nadu or Pondicherry under management quota seats or the state quota , although fees would be much higher compared to government colleges.
   
   
2. Deemed universities in these regions also accept students with lower NEET scores, but again, the fee structure is quite expensive.
   
   
3. Allied health courses like BDS , BAMS , BHMS , or BPT could also be an option if MBBS isn't possible with your current score.

For more precise details, participating in the state counseling is essential, as cut-offs vary each year based on seat availability and competition.