Can fibroid tumors cause symptoms farther away from the uterus?

Yes: If you have fibroid uterus and loose more blood every month you can have iron deficiency anemia which can present with weakness, shortness of breath on exertion and in some patients eating ice.All these symptoms can be corrected by propertreatment of fibroid tumour surgically and iron replacement therapy.

If they are large: Fibroids can cause bleeding from the uterus in some cases. Other times they can cause pain and pressure. This happens when they get large enough to press on another structure (like the bowel or the bladder). They would have to be really large to put pressure on anything outside the pelvis. So if the problem is in the pelvis, maybe. If it is in your chest or upper abdomen (belly), that is unlikely.