Was my mold issue handled properly?
The most likely reason for you feeling worse is leftover dust from the work performed. That will include dust from the drywall, from sanding the filling and especially mold particles from the disturbed wall. The room may look clean, but replacing drywall will produce a lot of tiny dust particles that will settle everywhere and make an allergic person feel really bad until the dust is removed.

It might also be allergy to the new paint components and if that's the case then the paint has dried by this moment and you'll feel better.

So the number one thing is to clean the room thoroughly - wipe everything where the dust and mold particles may have settled at least twice.

As to painting over. Latex paint will form soft yet rather strong film that will bond and contain the mold for a while. If there's any amount of humidity and mold is indeed in the wall then mold will continue to grow and will likely resurface at some moment. However until that happens you can feel more or less safe - the dried paint is like soft plastic covering and containing everything.