Did Einstein get paid for discovering the General Theory of Relativity?

Not directly.

He was, at the time he wrote his work on General Relativity, a professor who was highly respected by his colleagues but unknown to the general public; and thus earning a professor's salary. Due to his work he became, literally overnight, the famous scientist in the world. As such, he was much in demand by the public for various speaking and publicity engagements. In THAT sense, he received monetary reward for his work.

He later won innumerable honors for his work, some of which paid some money.

However, his big prize -- the Nobel -- was for the photo-electric effect.