Hello,
As you have not mentioned your category or state I'm mentioning the answer considering that you are asking for all India quota seat in general category. It is difficult to get a seat with this rank as last year the cutoff for all India quota MS General surgery was 8222. However, you have scored a good rank and have chances in your state under state counselling. Try to attend all rounds of state counselling in your state. For more information about neet of cutoffs check the link given below:
https://medicine-careers360-com.cdn.ampproject.org/v/s/medicine.careers360.com/articles/neet-pg-cut-off/amp?amp_js_v=a2&amp_gsa=1&usqp=mq331AQCKAE%3D#aoh=15809291249661&referrer=https%3A%2F%2Fwww.google.com&amp_tf=From%20%251%24s&ampshare=https%3A%2F%2Fmedicine.careers360.com%2Farticles%2Fneet-pg-cut-off
Hope this helps.
All the best.