Yes, those types of cysts are the type that are known to have been around since birth, but if they are causing symptoms, well, that means a change is afoot.
They used to drain them but then they just refilled (like any cyst) but now they remove all or part of the outer membrane so it cannot re-form.
If you check around, you should be able to find a doctor who is competent and will know how to treat it.