Can I get a divorce and child support in the U.S.?

We were married in the Philippines but moved to the U.S. shortly after. Our children were born here in the states in Chicago. I now want a divorce due to mental cruelty of my husband to me and my children. I don’t know if we ever registered our marriage here. Can I get a divorce and child support here or does it have to be through the Philippines? I need to know what my rights are. How will child support be calculated for my children?