Must I pray despite what is being discharged from me, or should I wait for a medical solution, or what should I do, especially since I am not regular in prayer due to coming out of the restroom and feeling something coming down from below that moistens the opening of the organ, which has made me refrain from praying for fear of not being in a state of purity?

If your feeling of urine drops exiting is merely an illusion, then pay no attention to it. However, if you are certain of their exit after urinating, then relieve yourself a sufficient time before the prayer until the drops stop, then clean yourself (istinja'), perform ablution (wudu'), and pray, even if you miss the congregational prayer. Beware of neglecting the prayer, and consult doctors regarding your issue.