KANSAS CITY, Mo. -- Quarterback Alex Smith missed a season and a half during his time with the San Francisco 49ers because of an injured right shoulder. So an abundance of caution led Smith to get treatment at halftime of last week’s game against the St. Louis Rams for what the Kansas City Chiefs are calling a sprained throwing shoulder.

“I’ve had a history of stuff with my right shoulder," Smith said. “I was a little sore, but I felt good.

“(He was concerned) enough that I went in to get some treatment at halftime and get it looked at. In the middle of it, you’re feeling loose and you kind of keep that swelling down and you’re feeling good. It was something I felt I could handle."

Smith, who injured the shoulder toward the end of the first half after being sacked, played most of the second half. He was replaced in the final minutes by Chase Daniel.

Smith was scheduled to practice and take his normal workload Wednesday as the Chiefs begin their preparations for Sunday’s game against the New York Jets at Arrowhead Stadium.

While it appears Smith will play against the Jets, his history with the shoulder makes the situation worth watching. The Chiefs didn’t feel Smith was putting himself at risk by playing in the second half against the Rams.

“He felt good enough to play," coach Andy Reid said. “Those kinds of things, they tighten up a bit on you after the game. He’s got a bruised shoulder. Those things happen.

“He was loose and he stayed loose. He felt good. The doctors looked at him to make sure he wasn’t going to be in a position where there was going to be further injury. He just landed on it funny."

In the Rams’ game, Smith became the first NFL quarterback in two seasons to win a game while throwing only one pass more than 10 yards down the field. Reid said he didn’t change his play-calling to accommodate Smith’s injury.

On that subject, Smith said, “I hope not. I certainly don’t feel like that. It didn’t need to be like that. I felt 100 percent and could do everything I needed to do."