It's hard to say since I don't know if that was a delayed reaction because your skin is sensitive, or if that whiteheads/closed comedones appeared as purging.
Purging often happens when your skin is introduced to active ingredients that cause chemical reactions and change in layers of skin, death of cells (retinoids) or sloughing off of dead skin cells (chemical exfoliation).
Purging happens when gunky stuff deeper within skin gets forced to the surface faster than it normally would do to BHA and AHA, so I think to really know, I would try salisylic acid again, no more than 2 days a week and see how it goes after a 4-6 weeks.
Often times skin has to go through getting used to new ingredients, then it will settle down when it gets accustomed to the product, or it will continue to flare up and be irritated if it does not like the new product.
It just unfortunately can take time to see if skin can become accustomed to something new, especiallly actives, when skin is sensitive because it can react to anything and be disturbed out of its norm very easily.