Hey there, With 243 score in NEET, yes you can take admission in private colleges in NEET and you also belong to OBC Category. Really that will be very helpful to you while taking admission in Government Funding Technical Institute (GFTI) as some special seats are being reserved for each and every special reserved category. If you want to check the colleges available for you then you can check at NEET College Predictor and it will be very beneficial for you.

 I would personally suggest you use the NEET Predictor and explore various colleges according to your category and home state quota and choose the best one for you as this college will be your future lifeline.

https://medicine.careers360.com/neet-college-predictor?icn=neet-clgpd_landing-page&ici=prediction-section_c360-home