Help! is it possible to have major depression and dysthymia at the same time?

In a way, yes: Someone can have dysthymia (persistent long term depression) that can become a more severe type (major depression) for a short time and then back to dysthymia. So, person can have both MDD and dysthymia though they don't occur at the exact same time

"Double depression": Although double depression is not a DSM diagnosis, many subscribe to the notion that it exists, notwithstanding. The patient presents with low to medium intensity chronic depression that does not waver all that much, but then the patient's mood can decrease to the pit of a major depressive low, then rise back up to dysthymia again. This is serious, and needs to be closely monitored with meds & tx.