Is it safe to throw the day after you work on upperbody(shoulders, triceps, chest, etc.) in the gym?
Yes, because you are using pretty much different muscle groups.
The only concern I would have would be for the muscles of your shoulders. They would get a workout in both cases.
For that reason, I wouldn’t go all out.
Yes you can throw the day after. The only thing i would watch out for is maybe actual pitching the day after because sometimes just a tight shoulder, as Chris said, or a tight back or chest could result into a change or mechanics which does lead to injury. A way to keep this from happening is to stretch stretch stretch. Also as Chris said your not going to want to throw around Max Out weight the day before. I think as long as you stretch before and after pretty much anything you do with you arm regarding throwing or stregenthing you should be okay. If you happen to feel a little bit tight ease up on the throwing maybe or just try to long toss which i found tends to stretch your arm out. Just listen to your arm if it hurts…ease up.