It's great that you know the dosage of your homemade tincture! The amount of tincture necessary to help with pain is different for every individual depending on their unique endocannabinoid system and prior experience with cannabis. In general, we recommend that first-time consumers or those unsure of their dosage "start low and go slow": start with a small amount of product, wait 20-30 minutes to let the full effects manifest, and then decide if taking more would be helpful for your goals.
For reference, 10mg of THC is considered a "standard" dose for edibles. If a dropperful of your tincture contains up to 15mg of THC, you may want to be careful about how much you take at one time!