Of course you should go to see a mental health counselor! You don’t have to suffer like this. What you are describing is consistent with a panic disorder or depression. Both are highly treatable. You may get some immediate relief from some medication, but for long-term results you also need to learn some new ways to handle those overwhelming feelings. For that you need a therapist who is experienced with cognitive-behavioral therapy and who enjoys working with teens. Ask your doctor or the school nurse for a recommendation.
I understand completely why your mom is so worried about you. I am too. You are missing out on your teen years. Get yourself some help so you can enjoy your friends and do well in school. You deserve it.
I wish you well.