Lost Names in Contacts

On my iPhone 5, I updated to 8.3. When i tried earlier, I got a message telling me that I didn't have enough room, so I went through steps to get rid of a large block of "other". (On the WikiHow website, it describes "How To Get Rid Of Other on the iPhone." I did some of the steps like "Deleting the Browser Cache and History," and "Delete Individual Message Thread," and "Deleting and Reinstalling Email."

I didn't do any of the other steps.)

I updated the software, and when I checked the phone, I saw that all of my previous text messages no longer had a name identifying from whom the message was from. Instead it was just the phone number.

I could try to figure out who the phone numbers belonged to by reading the messages, then creating new contacts for each, but that seems really tedious.

When I looked in the Contacts, I saw that the only contacts I had left were from my Facebook friends.

Is it possible to "restore" the iPhone to retrieve ALL of my old contacts? I'm reluctant to try anything for fear of losing the phone numbers from the earlier messages.

Is it possible to check my home computer to see if the information is still there?

Is there something in Settings that I may have inadvertently turned on or off?

Thanks for any help you can provide.

Gary