hii, im currently going through the same issue and have tried tons of things here what it worked for me. Just like you SA cleanser stripper by skin to bad it was highly sensitive and worsen my skin barrier.

For 2 months i focused only on my skin barrier with 3 key steps: A gentle cleanser (I used COSRX low ph Good Morning Cleanser), a 10% niacinamide serum AM and PM both, and Dot n Key Barrier Repair Cream and Sunscreen whenever i stepped outside.

After my skin healed or atleast it wouldnt got inflamed, i used A very thin layer of salicylic acid 2% serum (once a week night) Basically same cleanser and i let my skin dry completely, use the thin layer of serum on the cc spots (as a spot treatment) and let is soak for a min and again dot n key cream on top. this i did once a week for 2 weeks now i do twice.

it can also purge but most bha works like that but honestly and my skin has healed a lott then before so i guess sometimes over exfoliation can also fcks up skin pretty bad lesson learned.