Hi..
Welcome to HEALTHCARE MAGIC..
I have gone through your query and can understand your concern..
As per your complain it seems that you have generalized 
hyperpigmentation and the Rejuglow gel that contains Kojic acid, 
glycolic acid,arbutin, vitamin E and other constituents and it is an appropriate 
depigmentation formulation and you can even apply it all over your face while Hyclean contains 
Hydrocortisone and it should be specifically applied over the spots..
The products advised to you are appropriate and you can use them without any problem..
You can also wash your face with 
salicylic acid and glycolic acid containing facewash..
You can also exfoliate your skin twice a week..
You can limit sun exposure..
Drink plenty of water and take Vitamin C supplements..
Hope this information helps..
Thanks and regards.
Dr.Honey Nandwani Arora.