Thanks for visiting the Apple Support Communities merry313,
If you already have a Bluetooth mouse paired with your MacBook Air, you should be able to turn it on and use it on the Login screen to sign in. If you do not already have a Bluetooth mouse paired with your MacBook Air, you will need to use a USB-connected mouse to sign in. Once signed in, you can then set up a Bluetooth mouse with your MacBook Air from the System Settings, following the how-to steps here: Connect a Bluetooth device with your Mac - Apple Support.
If the built-in trackpad continues not to work, we recommend getting in touch with Apple Support directly. They will have the tools and resources needed to further isolate and troubleshoot what is causing it to misbehave. You can do that here: Get Support.
Have a wonderful day!