Is it possible for an std to come back within an month after being treated for it?

Yes: The original infection may not have cleared or you may have been reinfected. If having the same symptoms seek evaluation, make sure you tell them you were just treated.

Yes-several reasons: Keep in mind that an std that recurs, can be due to: 1.Inadequate duration of therapy 2. Reinfection from an infected partner (ping-pong effect) 3. Reactivation ( herpes) 4. Wrong original diagnosis requiring additional testing.