Will hooking up my iPhone up to another computer mess with my music?

I have the iPhone 5 and I hooked up my phone to my sisters computer because I didn't have a computer to hook it up to but now that I have a computer and I downloaded iTunes on to it will it delete my music?

No. The worst that could happen is you will put any music you have on itunes in your new computer onto your iphone. And thats if you sync all your music then its technically your fault but nothing bad comes out of that. Don't worry. But just remember to put all your music onto your iphone that you had on your sisters computer so that you can have that music in your new itunes. Hope i've helped.
Nic

No it should not, just sync you phone with your itunes account on your new computer.

I will say yes because this is your computer with all of your stuff on it and you'll need to sync this computer with your phone. If you have your phone set to manually manage your music and videos then there will be no problem but if you don't then yes there will be a problem - it will erase everything - when you try to sync it. I suggest that you sync everything with your computer so that your iPhone is synced with your computer and that way iCloud sync can work correctly and you can then also set up Wi-Fi syncing with that computer. If you, however, do have it set to manage your music and videos then when you sync your device with your computer it won't touch anything but it will make life with you new iPhone 5 much easier and open the door to many more features that Apple provides whether on a Mac or PC.