Does rainy weather make you feel claustrophobic and depressed?

No. Rain is a component of the water cycle and is simply water being deposited on the planet. Technically, this is usually a good thing. If people attribute their depressed mood or sense of claustrophobia to rainy weather, it has to do with how they are interpreting the rain. Just think, changing the interpretation could lead to a glorious feeling.
Perception. Dr. Smith makes excellent points about perception and rain. In many parts of AZ, for instance, people are very happy when it rains. Believe it or not, even a cloudy day can lighten moods here! what you're experiencing is an example of your unique temperament -- just the kind of characteristic that could help a homeopath find a helpful remedy to treat you (if you had a problem & wanted help).