BAMS

It's difficult to get admission in government medical colleges at this score. For government medical colleges, your score should be 400+.
All the best.

Dermatology is a specialisation which you can get only after MBBS.
You cannot get it after any alternate medicine degree.
But extensive remedies are available in Homeopathy for skin issues.

I would say you should give it a try. There is a big chance for you to be selected. Apply in multiple colleges and wait till the last cutoff list.
All the best.

310 marks for OBC category is a very good score to get admission in a college for BAMS, but exact cut-off score can't be predicted as BAMS admission is happening for the first time through NEET.

I feel BHMS is a good field. Nehru Homeopathy Hospital under DU is an extremely good college for the same. Homeopathy is gaining a lot of importance these days and its growing at a tremendous rate. So, Ayurveda switching these professions is a really good idea because of its low side effects and much lower cost in comparison to the modern MBBS.