Hello student,

Once you have been allocated a seat through the TNEA counseling it is unlikely that you can participate again in another rounds.If pursuing engineering is your only choice, seeking deemed university and private colleges for management quota is your only choice.If you have attempted jee even though you have not cleared the exam some deemed colleges like sastra colleges accept those scores like 70-90 for general category candidates.Other private colleges consider you HSC marks itself but there won't be any special reservations.You can check this link for details about private colleges in tamilnadu

https://engineering.careers360.com/colleges/list-of-private-engineering-colleges-in-tamil-nadu

Best of luck