No contest is saying "I'm not going to fight the charges in exchange for avoiding a trial and prison. I'll accept the punishment of 1.5 to 3 years probation and give you $4000." You come out at the end without a conviction but also without an acquittal.

The state is essentially blackmailing you into accepting punishment without being convicted. That's what plea bargaining is all about. Saves the state a lot of money that it would spend on trial and incarceration.

Ah, deferred adjudication. That's something a bit different.

The state has agreed not to seek a conviction in exchange for you agreeing to probation. At the end of the probation period, if you have successfully completed all the probation requirement, the charges will be dismissed and you'll not have a conviction on your record.

That's the key. You took prescribed medication to control a potentially life threatening illness. It backfired and messed you up to the point where you had no idea what was happening.

That's the defense.

OTOH, going to trial is a crap shoot. Especially when children are involved and you also have to weigh the $4000 against potentially spending $20,000 to $30,000 to litigate.

It's a decision that you are going to have to make on your own.

I suggest you forget about that public defender and get yourself a real criminal defense lawyer.