This is typical of that age. Not all little ones do it to that level--some more, some less, but it isn't because you're doing something less than right. She thinks she's part of you, her identity is still wrapped into you...so she feels the need to be physically connected to you.
Distraction is nice. Be careful though, they are perceptive and sometimes become even more insistant and panic when they sense you're not wanting them.
If you have a sling, a moby wrap, a maya wrap, or a pouch, I'd highly suggest putting her in it when you go places.
I've put my little ones in the actual basket portion of a cart when shopping--if the sides go up to the chest--and that helped a lot.
Also, try having her walk. They have those harness-type gismos at Walmart, Target, etc..., in the baby section you can put on your baby allowing them to walk and explore a bit but they're tied to you. I used to hate the way that looked (like walking a dog) but having as many children I do, I've realized it is a useful tool that allows a sense of independance for the toddler and security for the parent. Of course, like any other thing, there are times it'll be a lifesaver and times it'll be a flop.
It's normal though; she's normal for behaving this way, you're normal for not enjoying it.