If your dad starting losing hair in his 20's (as mine did) why would you attest to finasteride or even Saw Palmetto ? You're obviously worried about it, and can I guarantee that you stress over it so why not take action now ?
At 19 years of age (same as myself by the way) you're about fully developed, not everyone is but the majority of guys are. If you were to grow anymore, it would be negligible amount at best. Saw Palmetto is as mild as you can get with any kind of "DHT lowering product" and it's efficacy with regards to hair loss is also negligible at best. I suggest you educate yourself more on male endocrine functions and talk to a physician before making any rash decisions to start-or not start a treatment at this point. If you're concerned about growing more (height), go to a doctor and have an x-ray done to see if your growth plates are fused or not. If so than sorry about your luck but your stuck at whatever height you are. As for outward growing, hit the gym and eat right; you'll see gains on or off Finasteride. Instead of worrying, take control now before it gets worse. Start minoxidil and see where that goes, for all we know it could just be a maturing hairline and you won't even need finasteride.