@Sooraj
Since she had medical allegations against me, I, myself, filed application in court for my medical checkup by medical board,and the court allowed it.
I'm not a legal professional, but in my opinion you never go for any medical checkup without explicit order for the same from court. If your case is in family court, just produce the letter before the judge and ask for an order/direction restraining her advocate from sending such letters, and ask for filing application in court for your medical checkup if she has any such allegations.
If she has raised any mental/medical issues against you in her petition, first inform the court that you are ready for any medical checkup, if she asks for, and the court allows it. Even then she didn't file the application for your medical checkup, you can file application for your medical checkup to negate her allegations, if you wish so.