Hello there, hope you are doing good!

I would like to tell you that the counselling for both the courses BAMS and BHMS are held separately and on different dates, so yes you can do the counselling for BHMS and BAMS course separately. I am attaching a link that will provide you all the information about the counselling for both the courses.

https://medicine.careers360.com/articles/bams-vs-bhms#:~:text=The%20counseling%20for%20both%20the,course%20within%20the%20due%20date.

Hope you found this answer helpful.

Good luck for your future!