Frequently Asked Questions - P Visa
A "B" visa is appropriate if the artist will not be paid in USA, other than for travel and incidental expense.
You may be able to apply for a green card if you meet the requirements of EB-1, aliens with extraordinary ability or based upon a job offer, and of course, if a family-based possibility exists
If you withdrew your application, you were not deported. You could apply for a work visa.