I felt somebody touch my shoulder and I looked back, but nobody was there.
触る means "to touch." This means to feel. It's kind of similar but somewhat different and also uses a different reading, making this word very hard in some ways. Just think how it's rare (れる) for you to feel anything at all, but this time you are, so that's nice, I guess.
The word also means to touch on, not in the physical sense, but when you touch on a subject. That's why it also means to refer to or to mention.
The reading is totally different from 触る so don't let that fool you. In this case, you feel some fur (ふれ).