I am on a MacBook Air (13-inch, Early 2015) and I don't get an option to update my MacOS

Is your current OS completely up to date with no extra patches or security updates to install? You will not be able to download any later version of macOS if your current OS is not fully patched first. Your laptop can support macOS 12.x Monterey as long as you are not using an internal third party SSD.

How to upgrade to macOS Monterey - Apple Support

You can find installers for various versions of macOS in this Apple article (make sure to use Safari or a Chromium based browser such as Vivaldi or Google Chrome):

How to get old versions of macOS - Apple Support

Keep in mind that beginning with macOS 10.15+, macOS no longer supports 32 bit apps. If there are no 64 bit versions of your 32 bit third party apps, then it is best to uninstall those apps by following the developer's instructions before upgrading to macOS 10.15+. If there are 64 bit versions of your third party apps, then you will need to install the latest 64 bit versions. Make sure the third party apps are compatible with the version of macOS you are installing since some apps may not be compatible with later versions of macOS (especially Monterey since it is so new).

32-bit app compatibility with macOS High Sierra 10.13.4 and later - Apple Support

Make sure to have a good backup before attempting the upgrade just in case something goes wrong.

You should always have frequent and regular backups of your computer and any external media which contains important & unique data.

The Age of this computer will Govern what newer version of macOS it will Qualify to install. Use About this Mac from the Apple Icon on Desktop - the required Information will be there.

With the above information in-hand - follow this How to get old versions of macOS and verify what version this computer Qualifies to install.  For Best results use Safari to commence the download as Others may not work.

Safari will open a redirect and open the Apple Store where the download can commence

Tips Big Sir Upgrade Released Nov 2020. This computer does qualify for Big Sur

Tips Monterey Upgrade  Released Oct 25, 2021. This computer may qualify for Monterey but verify first.

Make Time Machine Backup  is very useful and can be used to Revert to Previous Working macOS

Notation - Mojave is the Last version to support 32 bit applications / extensions and Drivers. Catalina, Big Sur & Monterey supports only 64 bit and there is no workaround.

Suggest using Go64 to find 32 bit application before attempting the upGrade. Some or many of the Application already installed may required update or upGrades to 64 Bit Versions.

Are there any AntiVirus, Disk Cleaner, Optimizers, Un-installers, etc installed which should be removed as per Developers Instructions. They are useless, unneeded, cause havoc and interfere with the normal  operation of the OS and may even Corrupt the OS requiring a Reinstallation