Oral hairy leukoplakia (as you claim to have !) usually occurs due to weakened immune system.
It's unlikely to progress to a cancerous growth and usually it goes away after treatment of the underlying condition (improving the immunity)
Next Steps
If you're already in touch with your physician, he will guide you regarding treatment to improve your immunity.
Diagnostic tests are usually reserved for patients who's immune system is not weak and it consists of taking a biopsy. Costs may vary from one clinic to another.