Can I apply for disability benefits if I have used all my FMLA leave taking care of my disabled child?

Parents can't get disability benefits for their child's disabilities; they can only apply based on their own needs. If you have a disability as a parent, then you can apply for disability benefits.

Note that if you go on FMLA leave and don’t return to work after 12 weeks, you can be on the hook for the premiums your job paid for you while you were out. You may be able to take additional unpaid leave, so it's important to talk to the HR department at your employer if HR is helpful and not contentious.