You have stated that your marriage took place in the month of Jun this year and out of it you have been staying in your mother's home for the last three months.
It means you hardly stayed in your matrimonial home
No doubt you can take care of your ailing mother at least as a doctor.
But this will not stop you from discharging your duties to yor matrimonial people.
If you want to save your marriage you may have to adjust and live with your husband and in laws.
There is nothing wrong in the expectation of your mother in law that you have to remain in your matrimonial home and not that you have to run to your mother's place frequently.
Within one year of marriage you cannot file divorce case nor your husband.
Any petition filed seeking divorce shall be informed to you by the court by sending you a notice to that effect.
So you need not worry that your husband can obtain divorce without your knowledge.