What's the best way to treat a sunburn on your face without clogging pores and preventing pimples?

Cold milk. Cold milk compresses for 5 minutes to decrease heat amd relieve itching, non steroidal anti-inflammatory or bromelain for swelling and irritation and 1 per cent Hydrocortisone cream for a first degree burn. You experience relief within 12-24 hours.
Avoid sun :-) While most sunscreens are oil based, they should not have too much of an effect on acne. You may do better with the zinc or titanium oxide screens as well. Ideally wide brimmed hats, sitting in shade, wearing appropriate sunglasses, and avoiding excess sun exposure is your best bet. Be especially careful if you take Doxycycline for acne which can make your skin more susceptible to burn.