I am not a doctor, and the following does not constitute medical advice. It is only my opinion, based on various experiences.
Assuming that there is no serious organic cause - disease, deformity, or wound - the most likely cause of your back pain is shortening of the hip flexor muscles.
If we spend the majority of our time in a seated position - which most of us today do, the various muscles of the hip flexor group will shorten over the years. Cycling may be an otherwise fine exercise, but when you do it, you are in that seated position once again.
You may want to look on line for stretches for the Psoas muscle. One such strech is done lying on your back with your knees bent as though you were going to do abdominal curl ups. Then you lift the ankle of the offending side up and put it across the oposite knee. Then , grabbing the knee with or without the help of a towel, pull the knee toward your chest. Very likely you will feel the stretch right in the same area of your buttocks where you probably feel that a pin has been inserted. Just hold the stretch for a few seconds, then, without letting the knee move, contract the muscles of the painful side isometrically for a few seconds, then release. You will find that the stretch goes a bit further now. Hold for another few seconds and repeat, then hold for a final 30 seconds or so. Repeat on the other side.
There is also a stretch that looks very much like a lunge that you might find beneficial.
If your shoulders and back ar not too stiff, do a wrestler's bridge and just hold it for up to 3 minutes. If a wrestler's bridge is not possible, there's a stretch called a "table maker," or you could simply lie across one of those heavy vinyl exercise balls, face up.
Don't do just one of these stretches just once and expect a miracle do at least 3 different ones, and keep at it for a couple of weeks.
Good luck!