I think I might say, "I'm sorry, Melissa, but I'm SO busy these days!"
Then I'd roll my eyes, and shrug, and look exasperated (because I LIKE shopping and I always wish I had more time to go!).... "I don't EVEN have time to study !!!!" (This means I'm SO busy I can't even find time to study!)
Or I'd say, "I don't have time to go shopping because I'm so busy STUDYING!"
It depends on the reason for you being so busy.
And I like Richard's idea.. "what with..."
"What with everything else, I really don't have time to go shopping!"