Make my MacBook Air user account admin again

Here is an article written by a respected forum contributor which should allow you to do what @PeterChrisM was suggesting:

Restarting Setup Assistant to create Admin user account - Apple Community

If these instructions don't help to create a new admin user account, then you will need to perform a clean install of macOS as mentioned by @PeterChrisM.

FYI, after creating a new macOS user account, you will then need to fix what you broke on the old admin user account by using the instructions in this Apple article as a guide:

Change the name of your macOS user account and home folder - Apple Support

Keep in mind a clean install of macOS will destroy all data on the drive, so make sure you have a backup of your data. If you don't have a current backup, then you will have to do a lot more work to be able to access the data to back it up now that you don't have a valid admin user anymore. How this can be done may depend on the exact model of Mac involved since it may be impossible to access that data on a 2018+ Mac if you are unable to authenticate when accessing Recovery Mode.

You need to create a new admin user, 

reboot into Single User mode:

Boot to single user mode while powering up  hold down (⌘-S)

Launch Terminal and type exactly

sbin/fsck -fy  and press run or return

/sbin/mount -uw / and press or return

m /var/db/.AppleSetupDone

Restart

Setup Assistant should display and prompt you to create a new user. New user will automatically have admin rights. Should work for you.

A clean install,

Follow all the prompts

and you'll create an Admin account

Migrate all your files. (hoping you have a backup)

You should have 3 accounts, your old, the Admin (new) and a User. (No privileges)

but give your original account Admin privilages

It's a pain, however, but that should do it for you.