Is it permissible to perform Salah (Prayer) although one feels the need to relieve oneself?
A Muslim should not perform Salah while suppressing an urge to urinate or defecate. The Prophet (peace be upon him) said:
There should be no Salah in the presence of food or while suppressing an urge to urinate or defecate.
Muslim in his Sahih)
May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.