Temporary fostering a dog

Hello,

I’m fostering a dog for 3 days before deciding do adopt him. I was told that his owner passed away and since then he developed severe anxiety. I took him home but now I think they’re lying. He has sneezed once and he coughed gently a few times. He got neutered 4 days ago. I have anther dog of my own with chronic bronchitis and I’m managing that . Now, my question is, do people at shelter lie? Also, can this dog worsen my dogs condition if he has some type of respiratory disease? I’m so sad that I may have to take him back .