It sounds like your lower right back pain after biking could indeed be muscle-related, especially since it worsens with deep breathing, which can stretch or engage muscles in that area. This type of discomfort is often due to muscle strain or mild muscle spasms from physical activity.

• Consider resting and avoiding strenuous activity for a day or two to see if the pain improves.
• Applying a warm compress may help relax the muscles.
• Over-the-counter pain relief or muscle relaxants like those containing thiocolchicoside (e.g., Myoril) can be helpful but should only be used after consulting a doctor.
• If the pain worsens, becomes severe, or is accompanied by other symptoms like fever, numbness, or difficulty moving, seek evaluation promptly.
• Since the pain increases with breathing, it’s important to rule out other causes such as rib or lung issues, so consulting an orthopedic specialist or a general physician is advisable.

If you want, I can explain how to differentiate muscle pain from other causes of back pain. Meanwhile, please consider seeing a doctor for a thorough assessment to ensure appropriate care.To narrow down potential causes, we will need some more information.I understand you're feeling pain in your lower right back, especially after biking, and it gets worse when you breathe hard. Please tell me your age and gender.