Do I need to use 'gapps' in my email address?
In your college email address their is a gapps part which identifies it as a Google Apps account, but you only need to use this when you're working with Google, eg signing into GMail, or using GMail to sign into another website (this is called SSO, Single Sign On).
But you don't need to include the 'gapps' for anything else, if you would like to send email that excludes this redundant element, you can set this in GMail Settings > Account, you can imitate my settings below:
This will only affect email you send from the browser, if you want to change this on other devices you use (phone, tablet), you will need to do that in the respective Mail settings of that device.