I used to work in office cubicles and I liked it--it was added when before we had wide-open spaces with 40 desks all in view of each other. The cubicles were more private, gave us storage space right there, and were nicer than the wide-open areas.
You might make a list of positives about your cubicle. That might help you see it in a different light. Maybe you can make plans to visit with others at lunch, if you think that is what you are missing. Perhaps you have a touch of phobia about being in closed spaces--then, maybe a walk at lunchtime might be better.
It would be a shame to leave this job if you like it, to try to get another, and then find you are still unhappy, so perhaps it was something other than the cubicle.
Can you get up, say, once an hour, and walk around a bit, then go back? See if that helps.
Good luck to you!

