Might one have anxiety without physical symptoms?

Not usually. The mind and body are closely interwoven -- they are not separate. So when you feel anxious and fearful about something, your body responds by getting ready to run or fight: rapid, pounding heart rate; rapid breathing; sweating; pupils dilate; etc. Intensity of these symptoms might differ between people, and the interpretation might differ too ("heart attack! i'm dying!" vs "panic attack, okay").