Please make sure that if you try to put in medical reasons that are not genuine it may affect your future too. In case the present company puts in the relieving letter the reasons as medical issue with facts of the case, it may not be good for you. Do not precipitate the things just to get the letter asap.
Always good to stick to the terms of the employment which shows that you are an employee who can be trusted no matter where you work.
Thanks and Regards
If you are genuinely leaving because of health reasons, get a doctor to certify it. Attach the certificate with your resignation and get the same delivered to HR and obtain an acknowledgement.
Also write another letter address to HR with CC to your MD. requesting permission to quit without completing the notice period and your willingness to give 1 months salary in lieu of notice.
I am sure this will get you the desired result.
R. H. Kavarana