"I'm going to college every day" could be used to say you're at college every day (including working in there by yourself in a study room). If you're specifically talking about classes you could use "attending" instead, although that's unlikely since they typically aren't given every day of the week. "I'm studying every day" would be more general (it could happen at home), "I'm studying at college" would be more specific (people will probably assume you're studying if you're going to college, but you could be teaching, or not doing much).

You could say " I'm studying at (the name of your) college." when asked what you do for a living.