Hi aspirant,

      Yes you can apply for second counselling. You have fair chances to obtain a seat in this college according to your rank in the caste category. Do not worry and be confident in obtaining a seat in a medical college according to your choice.

The following are good private colleges in karnataka and tamilnadu coming under your need.

You can refer the following link to know more about the required college https://medicine.careers360.com/colleges/list-of-private-medical-colleges-in-tamil-nadu

https://medicine.careers360.com/colleges/list-of-private-medical-colleges-in-karnataka

Hope this helps

All the best