Desensitization

You have to force yourself to confront the anxiety head on. In small doses, gradually and deliberately force yourself to almost be late with something that shouldn't be a big deal but causes anxiety.

Fo that until you start to feel less anxious about it. Next step is to deliberately be late with something.

There is more to it than this, but this is the short version. Read up on it, it is what they do for PTSD.