I don’t have an iMac or a MacBook so I can back it up on that and I have an iPhone 7 and it won’t let me update it

Your question is a bit confusing - are you saying that your phone is full and you can't download the installer because it won't fit?

Without having a computer you will either have to find a friend with a Mac or a PC with iTunes, and update your iPhone with that, or remove content from your phone to make space for the installer to download. Apple's support document If you need more space for an update on your iPhone, iPad, or iPod touch might help....or ultimately buy a bigger iPhone.