Light sanding to evenly scuff the surface will not damage the carbon if you're careful. Unless you've got a nude carbon frame, you've got a few layers of clear coat and then a couple coats of paint before you get too deep.

Midwest: You applied too much paint in one coat. Many light coats, keep the nozzle sweeping back and forth, starting and stopping each application while you're moving. Let each layer dry.

Putting on too much paint at once and not waiting for previous coats to dry is what causes problems.

If you can get full coverage of a complex part in only 4 coats, you're probably putting it on too thick.