My family on my mother's side tend to live a long time. My great grandmother was asked why that was, and he attributed it to eating green onions on a daily basis. Whether or not that's true ,ions have a lot of uses.
Acne : Crush raw slices and mix with water, apply to the affected area. It may help for several reasons. The enzymes in it may act as a toner while other ingredients reduce swelling.
Bruises: There are a couple of ways to prepare an onion to help soothe the pain and inflammation of bruises. The first is to just slice it and apply the it raw to the breeze. The second is a little more ambitious, but could be equally effective. Dice half an onion and mix with salt. Get a cloth that is long enough and wide enough to cover the breeze, put the onion mix on the breeze and tie it on with the cloth. Leave overnight and the breeze should be much better in the morning.
Burns : To be honest, I can not imagine putting it raw on a burn, but it could work. There is an anti-inflammatory and pain relieving quality toions.
Insect Repellent: This could work two ways. The first way is to actually eat a lot of onions. If you like them in your cooking, that should not be much of a problem. The appearances will alter the way your sweat smells and it is a turn off for bugs. The second is to rub the juice of a raw onion all over your body. Either way they may repel something else … other people.
Splinter Removal: I have a hole in my leg from a childhood tangle with a cactus garden. Mom would think she got it all out and it would swell up and she'd have to go at it with a sewing needle again. I was four, and I remember it vividly. Imagine how I feel to know that I do not have to use the dreaded sewing needle again!
Tape a piece of raw onion over the splinter. You can use a bandaid, tape or any other method to keep it stuck to the site. Wait an hour and check. Chances are pretty good you'll find the splinter no longer in you but now in the raw veggie. If it has not finished finished working, you can repeat with a fresh piece.
As an herbalist, I know a lot of remedies, but for me the best are the ones you can get easily … and probably already have in your house. My knowledge does not do you a lot of good if you can not get the ingredients.