At some point I accidentally threw out the firework for the rocket and I couldn't finish the run, is there a way to get it back or do you only get one in total

You can't throw away items, only stock them. If you press X -> Right, there's a tile in the bottom right corner called "Stock" where you can find all the items you stored away.

Oh yeah, and some items like Heikichi's Firework get automatically stocked if you get them while your inventory is full.