Good morning. Well, like you said, your family problems were when you were little, which means they are over, gone. They will not come back again. It's history. Don't think about it anymore. Tell yourself that it's over, block out the thoughts of "What if it comes back?"
As for being afraid of losing loved ones, spend more time with your loved ones, and have more activities planned together, like on weekends. Every Saturday I go excercising with my family, then we go shopping. Spend a day every week or more with your family. As you spend more time with your family, you relax around them and will not be as tensed about losing your family members and friends. Also, tell them about your fear, they won't laugh at you, but instead they will reassure you that they are not going anywhere.
Well, it's good that you are able to accept going to councilling, it means you want to get rid of your problems. The reason it doesn't help may be because the counselors don't get your feelings. Maybe you didn't tell them enough, you didn't open up enough. Trust me, opening up to others will not 'cause any harm; instead you can feel better because you have someone to talk to about your problems instead of keeping them hidden inside you, which cause you to cut because you can't stand the stress.
Problems mostly are internal, if they are physical you wouldn't be facing a counselor, but instead a doctor. Like I said, in order for people to help you you need to trust them and tell them your problems. They may not help you entirely, things are still up to you, but they can make you feel better and give you suggestions.
Maybe you don't know that you are normal; but in truth actually everyone has the same problems as you and that's why they find you normal. Teenagers have loads of problems. Your teenage years are the times where you grow up so quickly and you may not be able to accept the changes.
Either that, or you are good at hiding your feelings and people didn't know you are struggling within yourself. So remember to open up to your closest friends. Or tell your parents that councelling isn't helping you and you would rather share your problems with them. They will be understanding; they are your family members after all. They want to help you so they suggested councilling, if you turn to them instead I'm sure they will listen. In fact, they may be more understanding than counselors because they know you better.
Maybe you want your mom to say goodnight to you every night, it may help reassure you that your parents are just beside you. Then you can sleep better. Have some stuffed toys on your bed. You can hug them and hugging stuffed toys make you feel so much better and they are so cuddly. =D
If you want help with your emotional problems, I'm always here and you can share it on ehelp, I will try to help you.
Good luck!