Can I have Medicaid and Private Health Insurance?

I'm 19 and have Aetna through my Dad's job, but can I apply to Medicaid as well? Google says yes but I am skeptical. I am currently stuck in a situation where I have no way of getting to my medical appointments. I live with my mom in the middle of nowhere, and I cannot claim disability because I do not yet have a diagnosis. There are programs in my area that provide medical transportation, but only for people who have Medicaid. My mom has already taken as many days off work as she can and can't take me anymore. We don't get any financial help from my Dad, I pretty much just have his insurance.