You're taking the right path by seeing a dermatologist in-person for any mole that has changed in size, shape, or color. 3 mm wide is pretty small for a melanoma, but not unheard of. Based on your photos, the growth rate is pretty slow.
Based on my family's history of moles & skin cancer, I'd say that's slightly suspicious rather than alarmingly suspicious, and I would keep the 6-week appointment. If it's causing you lots of anxiety, of course you might feel more comfortable moving it up.