Is it obligatory for me to give a monthly sum to the family after my sister's marriage and my mother's request for money to buy medicine?

You have done well by your sister by spending on her and helping her with the cost of medication, and for that, you will receive a great reward. The maintenance of your sister is obligatory upon her husband by consensus, and the expenses of her treatment are also obligatory upon him, according to the preponderant opinion of scholars. You are not obliged to pay anything to help her, but it is commendable to do so if you are not in need. If you are in need, then there is no blame upon you for not helping, and "the upper hand is better than the lower hand."