Is my prayer valid if I bathed, performed ablution, and prayed 'Isha after intercourse, without urinating before bathing, and then felt something sticky on my penis after the prayer?

Your prayer is valid, and you are not required to repeat it, nor to repeat the ghusl (ritual bath), because the ghusl for Janabah (ritual impurity requiring ghusl) has already taken place. What you felt after the ghusl does not affect their validity. Only wudu (ablution) is required for what comes next, even if it was semen.

Al-Qarafi said: "If semen exits after ghusl, Malik said: Only wudu is required for it."

Imam Ahmad said: "Because the desire has passed, and it is merely a ritual impurity, I hope that wudu will suffice for it."

In Majmoo' Fatawa Ibn Uthaymeen: "This fluid that exits after ghusl from Janabah, if there was no new desire that caused its exit, then it is a residue of what was from the first Janabah. Therefore, ghusl is not obligatory for it; rather, he must wash it, wash what it has touched, and repeat wudu only."