2% BHA twice daily in the morning and evening is really aggressive, especially if your skin isn't used to it yet. The dryness and tightness are classic signs of overuse. Your barrier is probably just overloaded right now. You're not doing anything fundamentally wrong, but the frequency is set too high.
Try this: reduce it to every other day or 3-4 times a week and see how your skin reacts to it. Then you can always ramp it back up once everything's back to normal. It's also important to use a good moisturizer afterward - the BHA alone will dry you out if you don't have a proper routine around it. A lot of people underestimate that. Give your skin a few weeks to recover at the lower frequency before you increase it again.