how to clean a piercing with a pustule?

my ~3 month old flat (implant grade titanium astm f136; end is 14k gold) has a pustule, being doing okay but was bleeding a few days ago after i was too rough removing a crusty/scab & now has a pustule (i had a side braid in on that side & i think my hair introduced bacteria/general irritation)

how do i clean this? been cleaning neil med but should i gently press this with some gauze/a makeup q-tip (making sure not to leave behind the q-tip fuzzies) to drain the pustule? it looks to be pretty fragile so i doubt it would need a lot of pressure