If they're fresh then there's pretty much nothing you can do to reduce them. Healing just takes time, unfortunately. So you will have to cover them up. For covering up you have two main options:
1. Wear a bandage over the affected areas. This may be a bit conspicuous, especially since the areas you've mentioned are quite typical self-harm spots. But remember if anyone asks why you are wearing a bandage you are under no obligation to tell them the truth. My personal tactic was always to say "Oh, I was in a knife fight with a shark" or something like that. Most people will not press you.
2. Wear something else. I understand that it sounds like you have a uniform you have to follow, but remember that the school CANNOT make you wear short sleeves if you don't want to. It is literally illegal. You can claim religious exemption if you like. The muslim girls in my school wore long sleeves all year round.
Your final option of course would be to skip the thing. Claim period pain, migraine, just don't turn up, whatever you like.
Stay safe