You havent mentioned your Category. Neverthless, the cut offs for various Categories in Self financed Medical Colleges in 2018 under General Category have been as follows:

General Category: 380
SC: 298
ST: 160
SE: 329

At 351 marks, if you belong to General Category  a seat is difficult. However, if you belong to Reserved Categories, you have a fair chance. Having said that, cut offs change every year and are dependant on various factors like no.of seats availble, no.of candidates appearing for the exam, top NEET score and difficulty of the exam. You can check the cut offs of various Categories at:
https://medicine.careers360.com/articles/neet-cutoff-gujarat/amp

Hello student,

As you have mentioned that you scored 351 marks in NEET 2019 and as you have not mentioned your category, assuming you to be of general category. Therefore as per last year's cutoff you do not seem to have any chance of getting a seat in self finance medical college in Gujarat. You can go for some private colleges.

Cheers!

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