What can I do if my landlord is embarrassing me and going in my apartment when I'm not home?

Except in cases of "emergency" (which the facts in your question did not indicate), the landlord may only enter after giving you two days advance notice. (See ARS Section 33-1343.D). If the landlord abuses the landlord's right of access, the tenant may sue the landlord for: (1) an injunction to prohibit future conduct AND (2) damages in an amount equal or greater than one month's rent. As an alternative to an injunction, the tenant may terminate the lease and vacate. (See ARS Section 33-1376). Before terminating and moving, however, I recommend sending a 10-Day Notice of Material Noncompliance. (See ARS Section 33-1361).