Yes, claustrophobia can can panic attacks. But by definition, when you get these attacks that are triggered by being in small, closed spaces, these are really anxiety attacks. Panic attacks are spontaneous and occur randomly- they don't need a trigger, whereas anxiety attacks have triggers, like with you and small spaces.
Anxiety attacks can have the following symptoms: racing heartbeat, pounding chest, increased breathing, shortness of breath, sweating, butterflies in the stomach, nausea, and lump in the throat. For more information on the differences between anxiety attacks and panic attacks, click here.