Puppy Blockage?

Puppy ate a piece of tree bark yesterday morning. He is a 3.5 month old frenchie. He showed no signs of straining, vomiting, or whining later on. He acted and ate like he usually did and didn’t show any discomfort. However today at 8 pm he vomited shortly after eating and running in circles over and over playing with a new laser pointer we got. I think he may have gotten dizzy but am not completely sure. He stood still for a bit and licked his upper lip over and over for like 10 times. After he vomited he made a hacking noise a few times. His vomit was green and had quite big pieces of baby carrots in it and pieces of his food. He swallows his food whole and never chews on it. He didn’t make the hacking noise before vomiting. An hour later he made the noise several times again. He is playing and eating like normal after and doesnt have any trouble pooping. He seems comfortable when i apply pressure to his stomach. I am just nervous its from the tree bark or something he may have ate we didnt know about. Or i may be overreacting and it is from dizziness after running in circles over and over. Right now he’s sleeping comfortably. Please help ❤️