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Yes, it is possible that back pain could be related to fibroids or various other uterine problems.
It is far more common for back pain to be due to back problems. And when there is a uterine problem that will cause pain, it is more common for that pain to be felt in the front of the abdomen or pelvis.
However, there is a quirk in how pain is felt in abdominal and pelvic organs, so that the pain can sometimes be felt in the back. This is similar to the fact that some women feel labor pains in the back, which is frequently called back labor. This is also sometimes called referred pain, although the term, referred pain, is not specific to the lower back and can apply in multiple locations in the body.
When someone presents to a doctor with back pain, the doctor will typically look first for back problems that could be causing the pain. But if the back evaluation does not identify a cause for the back pain, it is appropriate to consider whether the pain is referred from organs in the pelvis or abdomen, including the uterus from fibroids.
It would be atypical for a fibroid to cause lethargy or shortness of breath, but it is also unusual for lower back problems to cause lethargy or shortness of breath. Actually, lethargy can occur if a fibroid causes excessive bleeding and anemia, but it typically would not occur directly from fibroids.
Most problems that cause shortness of breath can also cause lethargy, but it would be appropriate to consider other evaluation for the shortness of breath.
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