Hey there, Luke!
Doing a backup is always recommended! Since you'd be doing a fresh re-install of Windows 10, you'd definitely need to have your most precious data saved somewhere else, otherwise, you'd lose it as a clean install basically formats the HDD.
If you don't have an external, you can try using other storage devices like DVDs or even an online cloud storage. This way you'd get at least some of your data backed up.
In the future, I'd strongly recommend you to consider getting an external HDD or some other storage device, so that you'd have another copy of your files and system.
Best of luck!
SuperSoph_WD