My start up disk is full on my MacBook Air. Is there a work around?

Your Mac needs a certain about of space to function, and warns you in advance of your startup disk filling up. Once it's actually full, it won't boot and options are limited. Try restarting in Safe Mode, and if it boots immediately empty the trash then delete files and empty the trash again (pick the biggest files you can). Start with media files you have them (movies take lots of space).

Start up your Mac in safe mode - Apple Support

If it still won't boot, try recovery mode:

About macOS Recovery - Apple Support

But in that case you're likely going to need to wipe the drive and reinstall macOS – I hope you have a recent backup from which you can recover your data.

Delete files, largest first. If you want to keep them, copy them to an external drive first. Movies, in particular, tend to take up space.

Find and delete files on your Mac - Apple Support

How to free up storage space on your Mac - Apple Support