How much time does a cross bite fix itself?

It doesn't: A cross bite is not self correcting. Please see a qualified orthodontic specialist.

Ortho Consultation: There are many techniques for correcting a crossbite in an adult. They all require orthodontic treatment along with other modalities (e.g. expander, elastics, springs, etc). I would suggest that you have an orthodontic consult for diagnosis and treatment options.

Cannot fix itself: Teeth need to be guided with sustained pressure to move. A crossbite is an occlusal variation in which the certain upper teeth are within the arch of the lower teeth. This can only be fixed orthodontics. Even after completion, they must be held in position with a retainer at night as they may tend to relapse depending on the severity of the crossbite

Forever: You must get braces if you want it fixed