I need to add a 50 amp switch for a new hot tub to panel but there is no empty space. Do I need a bigger panel

You may be able to install half size breakers, 2 in one slot. Need to have your panel looked at to determine if yours will accept these types of breakers.

What you need to be concerned with also is if the service and/or panel can accept the additional load of a hot tub.

My best advice is to have an electrician review your electric service before you purchase a hot tub to determine how breakers can be added and perform service rating calculations to be sure there is enough ampacity to handle a hot tub.

I agree but its also frequently quicker to just install sub panel because that isn't just a 50 amp "Switch" you need a GFCI breaker for hot tubs. Wiring a Hot Tub - Electrical Installation and Wiring Diagrams

You need an upgraded panel. Which has to be done by a licensed electrician.