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.

The feeling of wet numbness, tingling or burning pain is not uncommon early after breast augmentation.  This is caused by stretching and irritation of the nerves and should go away with time.

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.