Here’s my input (BUT all backs are different).
If the pain has just come on you may benefit from physio, so go for it. If it doesn’t resolve reasonably soon with physio, go back and INSIST on further investigation. (Blood test for systemic disease/MRI for mechanical problems).
Don’t let them fob you off, and don’t let them tell you it’s “because you cycle”.
I spent literally thousands of pounds on chiropractors, osteopaths, physios, acupuncturists, Alexander Technique, Pilates, homeopathy etc etc and I literally lived on painkillers – when all the time it was spinal stenosis and herniated (“slipped”) disks.
Surgery was the answer for me, it took about 8 months for the leg pain to go but now I don’t need painkillers. I wish I had kicked off sooner instead of putting up with it.
Hope yours is just a minor strain.