Hey there, I can tell you are upset right now. I know you want to be happy, isn't that all we want but sometimes life doesn't work out that way. We have to deal with obstacles we never wanted to face.
Your mum is now a single parent since your father past away and is probably finding it difficult to cope with your (and if you have any siblings) I'm sure she does want to be there for you but has to work to be able to provide you with clothes and food and all the essentials you need in life and you need to remember that. She is your mum and she will always love you no matter what happens.
Your mum may also just be very stressed over working and having too cope since you did say that she works all the time. But you need to remember she is doing this for you and you family and trying her best. Do you do any housework for her? Maybe you could start doing some for her, if you don't already. This may release some of the stress she could have with having to work, then come home to look after a house. It could also mean she won't be yelling and upsetting you as much as she has been. Also, doing little things like making her a cup of coffee or tea or something she likes after work to give her some time to chill out and relax would help her not too be so stressed.
Have you ever talked to her about how you are feeling? Perhaps, when you and her both have the time you could sit her down and have a chat. Express how you are feeling and that you want to be in her life more and want to spend some time with her and you feel like she isn't around to do that.
Also, she may still be dealing with the death of your father - her husband. Dealing with a death of a loved one if very difficult thing to do and achieve on your own. I get the feeling you aren't coping with his death also. I'm very sorry to hear you have lost him. I could only imagine the pain and suffering you are dealing with. Its important to remember that your father will always love you wherever he is and he would want you and your family to be happy. You could talk to your mum about you dad. Maybe sit together and talk about all the good times you and your family had while he was alive.
Cutting is something you should never resort too. It can really effect your life in more ways than we could ever think. Please check out this link. Its over 150 things you can do, other than cut; Clicky Look over the list and consider doing some (or all) of them to help you stop cutting because you don't want to be cutting. You have only started and eventually cutting becomes so addictive and you would find it extremely difficult to stop it. Please do go to this level and stop while you can.
If you had someone to talk to about your feelings and problems it would help an awful lot to help too you. What about some friends of yours? I always say go to a close friend you trust and can tell anything too. You should talk to someone like a friend about how you are feeling and maybe organise a few nights/days in/out too take your mind off your problems for a bit. Your friends will be here for you during this difficult time. They may also make your forget that feeling of loneliness you have been having because you know that you have someone to can always go and talk too whenever you need too.
You are having a tough time right now and I can tell you are. But, honestly life is never easy we all have our down days when we just want to give up but remember hold your head up high and stay strong. Good luck!