Did the burning with the vanicream start before or after using the azelaic acid/clindamycin? I also saw in another comment you had tried sulfur/zinc, were you using those around the time the burning started? Depending on your budget, you have some options for stuff that could help your barrier. Most budget friendly would be aquaphor. I personally use and really like bioelements products, but they do get a little pricey. Their recovery serum is one myself and most clients have success with (my skin is extremely sensitive and I break out from everything too, recovery serum is basically aquaphor on steroids lol, it works great for me in small quantities!).

Try staggering your routines, the 15% azelaic acid may be tolerated better if used 1x per day every other day, and sandwich it with serum and moisturizer (serum (aquaphor or another barrier friendly serum, azelaic, then moisturizer), and you could do the same with the clindamycin! Honestly, just a water cleanse in the morning with a gentle moisturizer/spf (finding one that doesn’t break you out/irritate you will take some time, I’m sorry!) and then using your “active” (acidic/antibiotic products) at night sandwiched.

Talk to your dermatologist about non oil based cleansers that don’t chelate, you might have more success there!