I wouldn't rule out the earwig. They can certainly inflict pain, possibly by nipping using their pincers at the end of their abdomen. After all, what's the point of evolving them if they can't use them.
I speak from personal experience. The latest occasion was when I was driving a few mopnths ago and I felt a sharp pain on my neck. When I felt where the pain came from I found an earwig. That wasn't the first time I've been bitten / nipped by them. On a previous occasion one nipped me with its pincers.
I don't dispute they can use the pincers to nip - but they won't usually nip repeatedly and don't leave the kind of marks that a biting insect will - the itchy, swelling type of bite which is normally an allergic reaction to bug venom or saliva. Still don't think this is the biting culprit - but there is something about them that's visually disturbing nevertheless!
Thanks jaguarondi and Big ma.
The night I was bitten I was skin generally very itchy all over not just on the spots. The spots are from my arms down to my ankles. I'm doing a through clean and sort of the room in question. My first thought was bed bugs but I have't found any carcases or faeces yet.