Is there any way I can apply for her to get a green card?

You cannot file an immigrant petition for your mother until you become a citizen. She can apply for an extension of her B2 status because of the need to continue her medical care in the U.S. The Immigration Service would ask for proof that there is no adequate care in your native country, for proof that you pay for the medical services provided to your mother in the U.S. and will continue to do so, and for proof that you provide for all her needs in the U.S. Extensions of status are granted for 6 months and, although the application is relatively simple, it should be handled by an immigration attorney in this case. If USCIS will not grant your mother an extension and she remains in the U.S. after the last date of her permitted stay, she will "fall out of status" - in other words, become illegal. Under the law as it is today, you will still can file an immigrant petition for her after you become a citizen, and her overstaying her visa will not disqualify her from receiving a green card. This exception exists today only for immediate relatives of U.S. citizens. As you might have heard, every Republican presidential candidate promises to reform the immigration law and policy, "tightening up the screws" on immigration. We can hope that it won't happen, but I cannot promise you that, by the time you become a citizen, the exception forgiving mothers of U.S. citizens for overstaying their visas will still be in force.