Can't sign into iMessage or FaceTime after updating to iOS 8.3

I recently purchased a brand-new iPad Mini 3 (actually just a week ago), and decided to update to the newest iOS since I hadn't done so yet with my iPhone. Thank God, I didn't. The update messed something up, and now I am unable to successfully log into my iMessage/FaceTime apps. I've tried reseting the network settings, rebooting the iPad, making sure location and automatic date & time settings were on, and logging in and out of my iTunes account, but nothing has worked for me so far. The farthest I've gotten is the step which asks how I would like to receive my messages/FaceTime requests (through phone number, iCloud address, etc.), but after hitting 'next', I am redirected back to the sign in page.

I can, however, successfully log into my iTunes account (which uses the same iCloud login), so I'm positive that I'm typing my information correctly. There also isn't a problem with my wi-fi--I swear.

What's worse, is that when I went onto my MacBook Pro, I noticed that my iMessages weren't sending at all, either. I logged out of iMessage, hoping to simply log back in again, but now it's giving me the old "Could not sign in to iMessage. An error occurred during activation. Try again."

The only thing I've updated is the iPad, so I don't understand why my MacBook is being affected, too. My iPhone, however, is working perfectly fine.

I'm sure I'm not the only one having this issue, right?