Excessive hair or hypertrichosis is a problem especially in females.In males facial hair are normal with some variation.Some may be little more hairy,with slightly more hair.This should not be considered as abnormal.So to take it as a problem,it depends how much excessive hair you have on your face.
Excessive hair loss may be due to hormonal abnormalities.To exclude this a hormonal assay is advisable.If you are taking orally or applying certain medications such as steroids,this may also be cause of excessive hairs.
Hair can be removed but the process is long and time consuming.There are topical applications which remove hairs temporarily.For permanent removal,two methods commonly used are electro depilation and laser hair removal.
I advice you a dermatological consultation.With good counselling i think you will regain your confidence and if necessary you can undergo hair removal treatment.