I'm very sorry you both felt so bad to start cutting. I have cut myself for about 7-8 years now and I can say you do get use to wearing long sleeve tops. For me I had no option as I cut high so had to wear long sleeves however you have cut you're wrists and you can cover them with bracelets, bangles watch, sweat bands or even those finger-less gloves that just has a hole for thumb and one other for 4 fingers.

You said it is close together so a watch may be able to hide it all, if not then a couple of bracelets and bangles should do the job.

I told my mum just after christmas and it went quite well, she didn't shout or anything which I wasn't expecting. You should tell you're parents but write a letter and give it to them, that way you don't have to be there when they see it.