After Bsc you can apply for medical exams only if you fall under the eligibility criteria of NEET. Yes you can apply for the entrance.
NEET entrance: The upper age limit for candidates seeking admission in MBBS/BDS seats was 25 years but as prescribed by MCI/DCI, minimum age of 17 years as on 31.12.2017 with no upper age limit and no limit on attempts. Applicable on All India Quota seats also.

Other exams you can give are:
AIIMS eligibility
JIPMER eligibility

Hope this helps you.
Good luck.