If you don't hurry, there won't be any tickets left.
Hurry and get them before it's fully booked.
早くしないと= if you don't hurry, if you don't hurry up, if you don't do it soon, if you wait too long
になっちゃう = (it) will (be), (it) will (become)
満員= to be sold out, to be fully booked, (there are) no tickets left
意味は同じですから、この例にいろいろコンビネーションができます。私ならこう言います: I'd buy the tickets now if I were you, before they sell out. (私だったら、満員になる前にすぐに買います。)