Aspirin will take redness down but not actually exfoliate which is what you need. The key is acid exfoliation, right cleanser can help but won't do all of the work, moisturiser can make it a whole lot worse if you pick the wrong one.
Basic program is:
Non-foaming cleanser such as Cetaphil, La Roche Posay Physiological Cleansing Gel, Avene Extremely Gentle Cleanser
Salicylic acid toner eg Clearasil pads, LRP Effaclar Duo, Paula's Choice 2% BHA
Moisturiser - oil-free, only if you think you need it eg Cetaphil moisturiser, Cerave. Oil-free SPF in the day time like Sunsense.
If not worked completely add in a retinol in the evening like LRP Redermic R, Avene Ystheal or Paula's Choice retinol.
If still not worked then you need a prescription.
Have a look at the Dr Sam Bunting Caroline Hirons video (best on youtube as the product recommendations are below), plus look for the Sam Bunting Q+A on here.
Heavy foundation is tempting but probably making it worse - Sam Bunting makes everyone dump their Doublewear as a first step. If you are a makeup wearer and want to cover up, have a look at Lisa Eldridge's acne video which is work of genius - she uses light foundation (as the rest of your skin is prob fabulous) with Vichy Dermablend on the spots and her model looks amazing, the before and after shots are stunning.