There is no medical explanation to why you will have a prolonged (several months?) residual side effect after stopping finasteride. Finasteride lasts in your blood stream for about a day. After a couple of days, it is essentially gone, but there is some tissue fixation which may keep it in some of your body tissues for about a week or so. The short duration for blood levels is why you need to take it every day for it to work. So if you had a side effect, it will likely subside within a few days (not months or years) after stopping the medication. Of note, side effects can go away even if you continue taking the medication.
I realize people write about libido issues related to finasteride (Propecia) and post concerns on the Internet. While I believe these people are having libido issues, I have a hard time believing that there is a direct correlation between finasteride (Propecia) and its long term side effects on libido. As a physician, I have followed and seen many patients over the last 10+ years who have been taking finasteride (Propecia) and I do not see the long term libido problem that people write about on the Internet. Yes, a small percentage of my patients (1 to 2 percent) may complain of sexual side effects, but the side effects usually go away after a few days or weeks (not months or years) and it is not permanent and a few canm not tolerate the drug for this reason. If there was such a long term or permanent problem with Propecia, I am sure I would have seen at least one patient in the last 10+ years describe this to me, and that has not been the case.
I strongly urge you to talk to the doctor that prescribed you the medication. The most important thing that people do not consider is that it may NOT be the medication that is causing a low sex drive. Many men (even in their 20’s) have sexual problems, but there’s not a great percentage of them that would admit it. While it may be easy to just blame the problem to a side effect from a drug, it can be a sign of a serious undiagnosed medical condition (such as high blood pressure, diabetes, depression, low testosterone, the presence of other diseases, etc). So although I appreciate the overall confidence many people have in me because I listen to (or read) what they are saying, you need a doctor willing to take you on as a patient — someone to meet with in person, not just communicate via email.