Entering university can be an exciting new phase in your life, where you will meet new friends, widen your social circle and learn new things in life. Thus I can totally understand your wish to clear up your skin at this stage .
Hyperpigmentations that occur after acne outbreak are called post-inflammatory hyperpigmentations or PIH for short, which can happen quite commonly especially in Asian and darker skin types.
Generally speaking, chemical peel (eg glycolic acid peel) is just one of the treatment options for PIH. Other treatment modalities include topical creams and lasers, while sun protection measures are also equally as important. All these treatments are suitable for your age.
Depending on the extent and severity of your PIH, topical creams with sun protection measures can be sufficient to see good results, and they are usually more affordable than chemical peels or laser treatments.
Though one can get a lot of information from Google regarding the various treatments of PIH, an experienced doctor can advise you on the most suitable treatment for your case, since every individual is unique.
For more information on PIH and its treatment, you can read more about them in my "Ultimate Guide to Pigmentation Treatment in Singapore".
Hope this helps!
Cheers!
Dr David Ng C H