I'm not all that up to snuff on the Medicaid stuff, as I'm wondering why they sent you to Medicaid unless you are "of age" for that. I'm also wondering how your younger son is on Medicaid, unless he is not a U.S. Citizen maybe.
But for you, if you did not have "any" health insurance for the last two months of the year, you'll be assessed a penalty for that on your tax return. The tax bill doesn't eliminate the penalty until 2019. That means that those who forgo health insurance for 2018 could still face a penalty. The penalty for not having health insurance this year is $695 per adult or 2.5 percent of household income, whichever is greater. Now I got this information directly from https://www.healthcare.gov/fees/fee-for-not-being-covered/ But that page assumes you don't have coverage for the entire year. However, I do know that things get pro-rated on a per-month basis. I just can't find anything on that.
Also, if you received a subsidy to help with the cost because of your income as estimated at the end of the year, your change in that estimation is what affected your eligibility of course. So in addition to a penalty for the two months of no coverage, if your AGI turns out to be much higher than the subsidy was based on, you'll find yourself paying back some or all of that subsidy too. This is just a "heads up" for a worst case scenario so you can be ready for what could be a big hit on the tax front.
But please read the web page above that I referenced, to see if you may be able to qualify for exceptions to penalties and subsidy paybacks.
My son has Medicaid since he born, he born USA so he is US citizen, I and my wife have insurance through marketplace. But when increase income on marketplace, marketplace kick me out and sent to Medicaid and keep my wife at marketplace because she has a green card.