Suicidal feelings or ideation is one of many symptoms of depression. You do not have to have all of depression's symptoms to be considered clinically depressed. Rather I do not tend to cry much (which is a symptom of depression), but I am still considered to have major depression.

I am glad you are going to see a psychiatrist. Your mother is correct suicidal feelings need attention. Try to be as open and honest as you can be with the doctor. I wish you the best.