Nose cartilage pain, no redness or swelling

Hello. About five days ago, in the middle of the afternoon, I suddenly had pain on the lower right side of my nose. if I didn't touch this area, the pain was about a 2 out of 10, but when I would press the outside of my nose at all the pain would increase to around a 6 out of 10. I had no redness or swelling, no nasal drip, and no pain across the bridge of my nose. This pain decreased the next morning and was gone by the end of that night, without any medication.

Today, I woke up with sinus drip, though that is now gone by the evening as I type this. However, beginning a few hours ago, I now have similar pain to what I had five days go. The difference now is that it's only located on the lower left side of my nose. Again, there is no redness, no swelling and no pain around the bridge of my nose. The other difference is that today is more painful than five days ago (5 out of 10 when not touched, around an 8 when touched).

I am in good health otherwise and am not on any medications. I keep trying to search to see what I may have, but everyone I find who describes this type of pain also mentions having swelling and/or redness, which I do not have. My only change in behavior is recently I have started to use a shampoo with tea tree oil in it, which shouldn't trigger this type of response (so far as I can find).

My PCP is on vacation this week and the other doctor in his office is not someone I have had positive experiences with, to put it mildly. Any insights or recaps of similar incidents are appreciated.

Thanks!!