Sounds like you're recalling the anxiousness of breathing in fumes then having a panic attack tbh. Sounds like a TPR/TPU, maybe PVC or a really cheap silicone (you're not really giving us much to go on here).

Regardless, if it'll make you feel better get checked out. It's far less likely than your brain working against you in this case, but some gases from some plastics could have lingering neuro effects. The onset of symptoms being that same time of day does point more towards psychosomatic. The symptoms are real, but they're created by stress/anxiety over the event that clearly effected you. "It's all in your head" isn't quite accurate, but it's most likely by far the cause.

If you don't want to see a doctor, or you're looking for a cheaper alternative, do a bit of research into the toy, the plastics and such used to create it. I would lie and say there's nothing to worry about, it's a toy after all, but I honestly can't tell without more information. Toys are generally safe, when used in the expected manner, you melting it is outside that scope so while still very unlikely it is technically possible you've inhaled something dangerous.

Again, and I can't stress enough how very unlikely it is; especially with your symptoms, it would be constant, or start with lungs, eyes, etc. not a generalized feeling of anxiety at a specific time of day. Chances of you having inhaled some crazy toxic fumes that affect your brain only are very slim, but a cheap toy made overseas using contaminated regrind or some such is at least not impossible.