Hello Agastya,
447 is a decent score and congratulations on that. As you have anyway decided to opt for private college, then there is no point of your category, whether you are reserved or unreserved. You can get a private medical college even after you have just qualified the NEET examination. As you have scored really good you have a 100 % chance of getting admitted in a private college.
Yes, the private college comes under state counseling hence you need to register for the state counseling and choose management qouta.
I hope this answer will help.
All the best for the future!!

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