Can I still be deported?

You are not alone. Thousands of people are in the same situation. If you came to the U.S. legally, it does not change the fact that you might not have legal status today. There is no immigration law that merely grants lawful permanent residency (a green card) to people that have unlawful status and have a United States child with a chronic illness. However, if someone is subject to removal proceedings (formally called deportation), he can defend the matter if he believes he can prove that he has lived in the United States continuously for 10 years or more, is a person of good moral character, and that a U.S. lawful permanent resident or citizen parent, spouse or child will suffer an exceptional and extremely unusual hardship (the defense is called "cancellation of removal"). Whether you have a winning case, depends on the chronic illness and other factors. If you win this case, you are granted permanent residency. If you cannot successfully defend your case, you might end up with a removal order and be deported from the United States.

If you have been in the US for more than 10 years you may consider filing for cancellation of removal. Otherwise your child can petition you when the child reaches 21. Cancellation is complicated and you should consult with immigration lawyer for advise.