It’s lovely to hear that you have some hops and are looking into how they can be used as medicine. You can harvest and dry the flowers yes. You can make them into a tea or tincture and they are sedative, with anti spasmodic, bitter, antimicrobial and some estrogenic action as well. This means that they can be supportive to menstrual cramping, tension headaches or other spasmodic/cramping pain. They can also be helpful for restlessness, general tension, indigestion (especially where there is tension and griping in the digestive tract, causing decreased digestive function). One caution is that they can make folks quite drowsy and even lean towards depressed mood if taken consistently.
I hope this supports your exploration of hops!