Is it safe to take the splint off my wrist myself?

No. Whoever put it on, needs to take it out. If it was done in an emergency room, you'll need to follow-up with a hand specialist, either a plastic surgeon specialized in hand or an orthopedic doctor specialized in hand.
Usually not. Splint is for immobilisation.Your doctor knows best as he did put the splint for specific reason.So, you should first ask him.If you can not find him and it is an emergency, you should go to nearest emergency room.