Is it normal that suck my finger and pull fur out of things to sleep

Ever since I can remember I've been sucking my left index finger and pulling fur/fluff out of things, such as teddies, fur coats, clothing, pretty much anything soft and furry, to be able to go to sleep. When I was younger, probably about 4 or 5 years old, I remember I went to my Nan's house and she'd hide anything that I can pick at, so I pulled at her cat instead. Poor thing. I've looked everywhere for the answer but have found nothing. I physically can not sleep unless I suck my finger at the very least, pulling fur is not essential to sleep but it makes me more relaxed. But I feel uncomfortable and wrong if I pull fur without my finger in my gob, though not the other way round. I wasn't breastfed or given a dummy when I was a baby.