What is the ruling on ritual bathing (ghusl) if there is rheum in or around the eye after completing the ghusl and going to university, and what is the ruling if something is found in the underwear and it is doubted whether it is semen or something else?

Any rheum (eye discharge) present in the eye must be removed before performing ghusl (ritual bath) or wudu' (ablution), as it prevents water from reaching the skin. If it is probable that the rheum appeared after ghusl, then the ghusl is valid. If the presence of rheum before ghusl is certain, some scholars hold that the ghusl and prayer must be repeated, while Ibn Taymiyyah considers a minor barrier excusable. As for what is found on clothes after waking up: if you are unsure whether it is maniyy (seminal fluid), madhiy (pro-ejaculate), or wadiy (post-urination discharge), you have the choice of considering it maniyy and performing ghusl, or considering it madhiy or wadiy and washing the impurity and performing wudu'. This is the view of the Shafi'i school and the fatwa acted upon.