Is it permissible to perform tayammum instead of ghusl after a wet dream, due to the restriction on showering in university housing to no more than once a week?

Nothing suffices to remove janabah (ritual impurity requiring a full bath) except water, when one is able to use it. It is not permissible for a person in a state of janabah to perform tayammum (dry ablution) unless water is unavailable or they are unable to use it. A person in a state of janabah must perform a ghusl (full ritual bath). If they are unable to perform ghusl in their current location, they must search for water to perform ghusl elsewhere to the best of their ability. If they are still unable, they may perform tayammum and pray, based on the Almighty's saying: "And if you find no water, then take for yourselves clean earth and wipe your faces and your hands with it."