This is a situation that hits very close to my heart. My first son was murdered by my ex-wife even as I'm righting this I can feel my palms starting to sweat...she is currently serving a 50 year sentence.
I don't know where you are, so I'm not sure if the medical card is different from state to state... here in Illinois, if you are unemployed & a single parent you can get the medical card. Check with your local welfare program see if you qualify...

I understand your conserns about being labeled an unfit parent, but that child is the first priority, & they may see you as being a good parent in that you were gutsy enough to face that to say I need help. The child here is the primary consern.

Were you working when you won custody? Do you have others around you that help you care for the child? I imagine between gaining custody & being unemployed, you are spending more time with your child than you ever have...

Are you stressed about any issues with you child?

Just as a word of caution....don't do anything stupid...if you hurt that child, you will get caught & you won't get leanency especially if you have not seeked professional help.

I don't say that to scare you, just as something to keep in mind if you get closer to feeling like you could follow through.

Frustration is normal...we've all been frustrated with are kids at some point...there is no shame in admitting that or admitting that it is harder than you thought.

We also have a healthy parenting forum here that may lend advise if you are felling overwhelmed about something...

I will make a sincere plea to you as a father that has lost a child in this way...feel free to PM me about any issues I will personally respond as best I can. You can let me know what state you live in & I will even research insurance options...