Your mum is half right. Facial treatment is good if the products used suit your skin type and gentle to your skin. Many facial treatments at salons may used generic products, and depending on the advisor, she may be only see what package you sign on, and unable to advise you the right products, or they may want you to sign higher prices package. cos higher prices must be better.
as you are still young, huge part of your acne problem is due to your eating habits, and also lifestyle habits, like sleep late, drink, eat processed food/ lack of balanced diet, etc..
I experienced redness and many tiny pimples during my teenage years too, cos lack of knowledge and use products without understanding my skin.. thats when i read up and attend skin care and nutrition classes to understand my skin condition.
I am doing facial at my home now, started with my friends and through word of mouth, I expanded to the public, due to positive comments from my friends. PM me if you require more details. I can do an assessment on your skin and advise you better.