For having no actual training your not doing too bad, you've got some pop already in your punches, considering how many guys I've seen at the gym flailing away with their home schooling.....
That said, its obvious that you have no actual training and thus your title 'punching form sucks' still is very applicable.
Here's some starting issues to work on:
a)punches should go out and they should snap back. You are throwing the punch and its ending up down near your waist, and then you slowly pull it back. You'll get creamed like that. Straights go straight out, and straight back, hooks swivel and then pull right back...you should always end up right back in guard position.
b)you are turning your head and following your fist rather than keeping your eye on your target (and since your fist is ending up down near your waist, you end up looking down after the punch). With very few exceptions, always keep your eye on your opponent, you don't want to be caught admiring your punches.
c) you are off balance after you throw each punch...I could not see your back foot, but your front foot wobbled at the end of each punch. Footwork is different for different punches, so I'm not going to get into those details, but for starters, bend your knees so you are not off balance, and working on the previous point about throwing the punch and then bringing it right back will help address the balance issues.
d)you are also bending your wrists excessively in the guard position...if you have them like that and start hitting a heavy bag, you'll have problems.
There's more, but I think those are the first items that jumped out at me.
If its possible, my best advice would be to find someone who can help you with your footwork for starters. Thats the foundation for everything else, so thats the first thing to address.
After you get some footwork training, add in shadow boxing as well. You should learn the basic three punches (straight, hook, uppercut) and then go through them all, slowly and just in the air, over and over, each day besides working them in the gym.
Unfortunately, I think there are too many little details to try and train yourself or be trained over the web if you are thinking about actually competing.
Hope some of the above helps though.