I'm not familiar with Elflora specifically. What I will say though is that most ( in fact I think all) prescription meds it doesnt really remove the hair, it just makes it lighter and les noticeable. Stop the meds, and it will come right back. Many of these medications are hard on the liver especially and doctors are hesitant to prescribe them long term for this purpose, and, it's not good for you.
Electrolysis on the other hand removes the hair, permanently. As one of the rockstar electolysists around here is fond of saying, once the folicle is dead it is not ever coming back, we dont grow more folicles.So once the hair is successfully treated with electrolysis it's gone for good. It seems to me , this is much healthier approach than meds are.
That said, have you considerd why the hair is showing up? In alot of cases it's because of excess testosterone rearing it's ugly head. In genetic females, that is sometimes caused by something called PCOS, Poly Cystic Ovarian Syndrom. Basically it's the eggs of your ovary, not being mature enough to release and them turning into multiple little cysts. If you have irregular periods, this would also be a good reason to check with your doctor and have some blood tests.
I suspect Elfora is something called an antiandrogen, it definitely sounds like it works that way. Antiandrogens are often prescribed for people with PCOS.