Hello

Firstly if you really want to go for NEET Examination then surely take a gap year and hard work and gain your marks and get admission in your favourite Medical College because nothing is impossible if you insist your parents and convince them that you are doing well for your future so, may be they"ll understand and agree to take a year, It's my suggestion

And if you want to take Mathematics after 12 you can also take it by give exam of the subject of your interest through NIOS( National institute of Open schooling) of class 12th.

If you cleared your exam, then you will be considered as of the subject in which you have passed in class 12. Also NIOS is equal to CBSE or any other equivalent board which means that it both nationally and internationally recognised and also age is no bar in NIOS.

All the best for your bright future ahead!

Happy learning..