Hi there!
You shouldn't encounter any issues by applying to the same universities. It could be a good tactic to overcome homesickness if you were to be together! When booking accommodation you may be able to request that you live in the same flat as well depending on courses (and if you want to live together of course!)
Of course, there is the chance that you may still choose different universities when it comes to replying to offers so I wouldn't completely advise choosing just so you can be together, its definitely worth doing what you want to do and where you want to go as you both may enjoy different aspects of both Sheffield and Nottingham.
If you haven't already I would definitely recommend attending Open Days so you can get a feel for the universities you want to apply to and if they feel right for you.
I hope this helps!
Daisy- Graduate Advocate🙂