Does accident proneness exist?

Well, probably it does. Some people seem to be more prone to accidents (with injuries requiring medical attention) during most of their lifetime than others : see a review/metanalysis here. Just statistical data.

And what about multiple accidents in a row happening to a person, but 'clustering' in time?

This is my accidents/injuries list of the past week :
Last Monday I slightly burnt my arm when taking a hot dish from the oven. I held the burned spot on my arm under cold running water for some time, and after all, it was not so bad.
On Wednesday, in my office, I bumped my knee into the sharp corner of a metal drawer of my desk: big bruise, all colours of the rainbow by now....
On Thursday evening, when washing up the dishes, I cut my wet hand on a sharp knife. A lot of blood, but a bandaid did the trick.
On Saturday, when vacuumcleaning, I hit my toe – hard - on a table post. Sharp pain, you know how intense this pain can be, and it still hurts a little now.
And finally, yesterday, around 5 pm, the culmination point (at least, I hope so!): when helping unpack, move and install new furniture at my sister's house, an angry heavy garage door decided to fall with its full weight on my poor head (defective mechanism – nobody could foresee). I was knocked down to the floor by this really serious blow, managed to crawl upright after some time, and everything in the next 2 hours seemed to happen in slow motion... My family wanted to drive me to hospital, but I refused. I just wanted to sit and lie down, and be left on my own, and rest and recover. I didn't lose consciousness, but my sight, hearing, muscle coordination, etc.... seemed to have gone into a kind of 'safe mode', only allowing basic impressions and movements. Two hours later came the nausea, and I threw up once. After that I felt better, but, after 10 minutes of heavy shivering, I was left with a serious headache and felt extremely tired. Later last night I tried to watch television, but something was wrong with my vision. So I went to bed after taking a paracetamol, and had a good night's sleep. When I woke up this morning, I felt better, but my head, right ear and eyes were hurting, and I had this weird sensation of cold in the area on my head that received the blow. So I went to see my doctor: concussion, of course. 3 days of rest at home.

Until Saturday I thought I was just being a little clumsy, although not exactly more stressed or tired than normal. That stupid accident yesterday, however, that could have happened to anyone being at that place at that exact time. Not caused by clumsiness, or inattentiveness, or whatever. It just happened to me.

Any warning from the universe involved? One could wonder.
But I think I'll stick to 'coincidence' as an explanation for the time being.... and be very, very careful in the next days....