Is it weird or uncommon for the breasts to feel wet and then when you feel them they're not actually wet?

Unusual sensations are common in the first several weeks. After 3 months,this would be a very uncommon and
hard to explain. It doesn't sound serious and I would wait until your scheduled appointment to ask about it.

I have had several patients feel like water was running down their chest after breast augmentation, some even feeling like it was inside the chest not on the skin. This is just from the nerves being stretched and the brain misinterpreting the signals. It will subside with time.

Surgery can cause abnormal sensation due to the disruption of nerves.  It is likely that this sensation is temporary.  I haven't had patients describe this to me, but it is unlikely that is anything to be alarmed about.  Please talk to your surgeon on Friday about this, but I think it can wait until then.