You did well by taking a ritual bath (Ghusl) when you woke up after having a wet dream. After having a bath, if what you discovered was sperm, which is a white thick fluid emitted by a male or a female as the result of sexual ejaculation, then you are not obliged to perform Ghusl again, because it is pure according to the correct opinion of the Muslim scholars .
'Aa'ishah said regarding sperm: "I used to remove the sperm from the clothes of the Prophet and he would pray wearing the very clothes after that." [Muslim]
However, if the discharge was urine, then it is obligatory to wash ones private parts and clothing and perform ablution before praying. The Prophet said: "Allaah will not accept a prayer of any of you if his ablution is invalidated until he performs ablution again." [Al-Bukhari and Muslim]
The same thing applies if the discharge is Mathy (pre-seminal fluid). Mathy is a thin white sticky discharge caused by sexual stimulation.
For more benefit about the rulings regarding, Maniyy, Mathy, urine, and Wadi (a thick white fluid that comes after some people urinate), please refer to Fatwa: 82518.
Allaah knows best.