You have two possible solutions available;

One, grab a tub of vaseline, a water hose and a vacuum cleaner before ingesting Tightson's Potion of Loosening. Of course, that will result in every orifice in your body, from pores to mouth, going completely slack & loose for a period of 12 hours, which may be unpleasant.

Two, swallow your pride and go to see a doctor. It will be painful, humiliating and your x-ray may end up on the internet, but your wand will come out eventually.

Now, normally I would say to just pull it out, but that may be inadvisable given that that may cause a magical discharge straight up your rectum. Oh, on a totally unrelated note, you should refrain from shouting, cursing or muttering angrily while this is taking place. You do not want to find out just what spells use 'fuck you, you fucking cunt' as the activating incantation.