My teen is accident prone

Our house has one main heater. A gas heater in what we call the "family room" use to be called the "School room" but the kids work more in their rooms now so we changed the name. Anyways, the room is more like a "den" for most houses, if they have one. It use to have a full working fire place in it, but that was closed off a long time ago. I don't know how long, our house (rental) is very old. Like my grandparents would have lived here when they were young kinda old.
Anyways, the fireplace mantel and such are still there and a gas heater was installed to heat the entire house. (I think it also use to have a furnace but it doesn't work and I don't know why) Our landlord doesn't like to put money in this place unless he has too. But, we have plug in heaters in the front of the house that are on all day to heat up the front cause the heat from our gas heater just can't make it that far. Plus theres a lot of drafty windows and doors that the heat escapes through. Well, we turn the plug in heaters off at night, for safety. So our oldest (13), who has the furthest bedroom from the family room will sleep on the floor in the family room when its too cold in his room. Well, we've been here 2 years and haven't had any problems. Until last night. When ever our son sleeps in the family room we tell him to be careful and not get too close to the heater in case his blanket falls in through the grate things covering the front or something. Well sometimes he will move a lot at night. And last night he moved in his sleep and got real close to the heater. He reached out to stretch in his sleep and touched the heater with the back of his hand.
So, this morning when I got up he tells me about it. Didn't wake me up, just took care of it himself. He said it was buring so he put an ice pack on it, wrapped it in a gauze wrap and went back to sleep. When I looked at it this morning it looked pretty bad. Big red spot and in the red spots he had a bubble of burned skin with the fluid and a spot with no top layer of skin. We put some aloe on it and he says he's fine. I don't think I need to take him in but we're gonna keep an eye on it a few days.
He is so accident prone right now. A few weeks a ago he was walking up the carport steps, slipped (probably cause of big 10.5 size feet) and hit his knuckes on the brick wall and scraped them up pretty good. Then a few days after that he was using a can opener. A manual one, cause our electric broke and we hadn't gotten another one yet, and we figured it wouldn't hurt for him to use a manual one for a few days. Ha. We were wrong. Some how he manages to break the can opener and in doing so he cuts his knuckle next to the scratches from a few days before. He cut down almost to his bone too. He bled and bled. We cleaned it and kept it wrapped a few days then alternated it between opened and wrapped, while still cleaning it. Didn't help. Its a few weeks later and its still healing caus we've had to drain puss from it a few times. I drained what I hope is the last of it yesterday.
Whats sad about all this, is its the same hand for all 3 accidents. When does the acciednt years end?