Is there a link between anxiety and changes in stools?

Oh yes. The same neurotransmiiters and receptors in the brain (serotonin, Dopamine and others) also occur in the gut. Some people get loose stools with anxiety, or frequent stools, some get constipated (more common with depression); "butterflies in the stomach", being "scared -----" show the effects of mental state on gut function.
Possible but. ...You should first be thoroughly checked by a physician. If all is well there, disturbances in bowels are a fairly common psycho-physiological reaction to stress. In addition, some medical conditions affecting the bowel can be aggravated by stress.