If you haven't applied it to those areas, then no.

I've been using 5% BP for 3 years and put it all over my face avoiding the eye area. However, under my eyes is always red and puffy and I have a very pronounced tear trough (the line that goes from inside corner if eye across the cheek towards the ear). Is this because of BP?

have you ever used sunscreen? Something like 90% of wrinkles are caused by sun damage. Maybe that area is just very dry though.