No you can not just "replace the breaker." First you can't just replace a 110 with 220 and expect things to work at all. Second, you aren't even legally (and safely) allowed to increase the AMPERAGE (i.e. from 15 or 20 to something higher) without upgrading the wiring to something that can handle that much amperage.

You need to add an additional circuit.

Get an electrician to upgrade the wiring in your shop. Your question indicates that you are not qualified to handle any part of this as a DIY project.

You will burn down your shop if you tinker with this, hire someone please.

You are overloading the circuit.

There is no way to "correct" this. You need to get a competent electrician in to add a circuit if there is room for it in the panel.

If you want to understand what is happening here, find the amp rating on that breaker. 15 or 20 amps probably. Look at each appliance for its amp rating. Add up the ones you are running when it trips. Guarantee they will exceed the amp rating of the breaker. You can't increase the breaker rating without different wiring, so it's better to just add a breaker and circuit.