Quit my internship after a month?!

I got an internship about a month ago in a customer relations position.

Since arriving at the company, I haven't really felt like I've fitted in (they are all lovely though) and the job is not what I was expecting at all - it's very sales heavy which was not how the internship was advertised at ALL.

Since about the end of the second week I've cried nearly day and it is making me incredibly miserable.

I would try and stick it out if it were any shorter, but I still have 6 months left and I can barely get up in the morning. I also want to go home at lunch time because my days are making me so miserable.

I've previously had a job I loved, and I just wish I could still be in the same industry (higher education). I know sales isn't for me, and I can't stand going to work everyday.

Is it fair for me to hand in my notice tomorrow after just a month? I really feel there is no way I will be able to survive the next 6 months.