Hello
Vaseline is basically emollient which seals the moisture in the skin and if you have increased sebaceous activity as you are describing as breakouts, there are chances of you getting breakout after applying Vaseline
As your skin seems like combination skin, a proper CTM routine might work
Using moisturiser immediately after chemical exfoliator would actually reduce the effectiveness of chemical exfoliator itself
Next Steps
Consult me via practo pro to get tailored made skincare routine which works for you to achieve desirable results