Crape Myrtle Disease
This looks like it is possibly an insect issue. To be sure in the identification, I would need to see a sample. If possible send a small branch with the symptoms you see on this to the cooperative extension office in Georgetown (Carvel Research and Education Center).
I suspect it is a soft scale and could be treated with commonly found insecticides at garden centers or box stores. If possible as a minimum contact the extension office at Georgetown (https://www.udel.edu/canr/carvel/ and https://www.udel.edu/academics/colleges/canr/cooperative-extension/directory-contacts/sussex-county/). The person best for you to contact would be Tracy Wooten and then she can contact me as a follow-up.