How long has this been going on? How long does it last? Do you notice it at specific times during the day?
I'd have to say that it's not a "normal" thing or we'd all be experiencing this, but it's certainly not unheard of.
From the description of your symptoms, in my humble and non-medical opinion, I think you're dealing with a pinched nerve which can interfer with the blood flow. When blood flow is restricted, the symptoms of tingling and something crawling on your skin is very common. When the nerve is not being pinched, your arm probably feels quite normal. I'm sure you've woken up with a "dead" arm......we all have...the result of sleeping in such a way that we've cut off the blood supply. As the blood flow returns, we can feel a pins and needle sensation and sometimes a painful tingling.
Your problem could be the result of an injury to the shoulder, elbow, wrist or fingers. There are other reasons this could be happening which is why you should consult your doctor..........only he/she can tell you exactly what's going on.
I wish you the best
Peace
Greenlydia