There should be a few things you can do while in these 2 things like just look at your bank and stuff,

And the main thing you should be able to do is buy favors and respected days.  Why cant you do this while in infirmary?

You SHOULDNT be able to do anything with your bank account while locked up. As for upgrades, it basically comes down to the fact that you can't browse the prison in the infirmary

OK I see the bank account thing.

But just clicking Become Respected?  Its not a a big deal I guess just something I thought.

I hear ya, and going direct to the upgrade pages should work no problem, it's just going there via exploring the prison WONT