First -- be sure to stay up to date with your existing medical insurance. It is far LESS expensive than any new private insurance if you could get insured at all.
Furthermore, you may find that your current insurance offers far better benefits and better access to doctors and services than any Medicaid program.
$3500/year is not a terrible out of pocket expense vs some alternatives.
Second -- You can begin to explore what your Medicaid options might be on this link: http://www.cms.hhs.gov/medicaideligibility/
I wish you the best!
**All above answers are provided as general information only. No warranty is made regarding the fitness or accuracy of the information provided in this answer. You should seek advice from a licensed CPA, attorney or CERTIFIED FINANCIAL PLANNER™ as to your unique financial situation.