Electrolysis has been already proven and certified by FDA as a permanent hair removal method. It is very effective and unfortunately also expensive. It is done by some small needle insertions into the skin, that causes destroying of cell responsible for hair growth.
There are different types of electrolysis. What is important to mention here is that electrolysis can cause scarring.
Hormone treatment and oral contraceptives
There is possibility that abnormal hair growth is in your case because of hormone imbalance. Your doctor can check it. If that is the problem you will need to use a hormone treatment or some oral contraceptives as it may be able to return your normal hair growth.
Then you don’t need any special methods to remove unwanted facial hairs, it will disappear by itself. You need to talk with your family doctor to know all of the options.
Of course when your hairs are growing in strange places or if it not only abnormal hair growth but there is far too much of unwanted hairs on your body, you should contact your doctor. You will need to make an appointment and discuss a situation.
It can be you need to do some examinations to check if there is no serious medical condition associated with abnormal hair growth.
So if you have problem with abnormal hair growth the best option is to try first homemade, natural methods to get rid of unwanted hairs. These methods are cheap and simply, most of the time they are also effective so it is worth to try to use them.
If that will not work for you or the problem with a strange facial hair growth will get even worse you should meet with your physician as fast as possible. You need to discuss if there is no underlying a medical problem. Maybe some medications can stop your unwanted facial hair growth very fast.