I am in Texas, my father is currently disabled and is supposed to be paying child support. Can I still collect my back child support from the government?

Do you mean can they take child support from SSI checks? I believe they would be exempt.

From the government, no. What is the support order currently in effect? Has it ever been modified in light of your father's disability? If not then it's still in effect and your father is responsible for paying in full, including arrears. If it has been modified or terminated, you still may be entitled to payments prorated to the date it was actually modified or the date your father became disabled and (I presume) unable to work. Your father, not the government, would be responsible for paying this. You can garnish his wages (if he still has any to collect), intercept his tax return or place a lien on any real assets he owns as means to collecting what's due.

And of course actually your mother or guardian who has custody of you, has to do what has been mentioned.

If he has no job, only SSI income and does not own property there is little you can do to collect anything