Why was Silas breathless?

It looks like your question pertains to chapters 12 and 13. In chapter 12, Silas finds a body in the furze bushes.
In chapter 13, he runs to the Red House to get the doctor. Silas is breathless from the combination of physical exertion and the shock of his discovery.
We also learn that Silas first discovers a baby girl (whom he later names Eppie) before he sees the apparently dead woman in the bushes. Silas runs for the doctor because he cannot be sure that the woman is dead. At the Red House, Godfrey is shocked to see Silas running in with a child in his arms.
Interestingly, Godfrey immediately recognizes the child as his own daughter. The text tells us that his "instantaneous impression" is "unaccompanied by doubt." As for Silas, he tells Mr. Crackenthorp that he wants the doctor; he has just seen a woman in the bushes outside his cottage, and he believes that she may be dead.
Mr. Crackenthorp goes to fetch Mr. Kimble (Raveloe's doctor). Meanwhile, Mrs. Kimble tells Silas to leave the child with her and the other ladies. Unsurprisingly, Silas refuses. He maintains that the child came to him and that he has a right to keep her.
As for Godfrey, he is secretly relieved when he discovers that the woman is dead. She is, after all, his first wife, Molly, the woman he is secretly married to. With Molly dead, Godfrey thinks that he will be free to court the lovely Nancy Lammeter. He also rationalizes that it would do no good to dredge up the past now, especially when happiness is within his grasp. As a result, Silas adopts Eppie, and Godfrey is left experiencing a strange brew of emotions, from jealousy to guilt.