GLP-1 medications change how quickly food moves through the digestive system. Some people experience slower transit (constipation); others experience faster transit and loose stools, especially early in treatment or after a dose increase.
Diarrhea is often temporary. The main risk is dehydration, which can affect the kidneys, so fluid intake matters. Diarrhea that occurs most days rather than only around injection day is a reason to contact your provider.