Running very rough

I tend to agree with you. However, these engines typically don't have vacuum lines exposed very well, especially on the undercarriage of the vehicle.

Here is how to test for a vacuum leak so let's do this and rule that out first:

https://www.2carpros.com/articles/how-to-use-an-engine-vacuum-gauge

The next thing you want to do is lay on the ground and look for any damage. Clearly if you just ran over a deer I wouldn't expect serious damage but hopefully we can find the general area that it hit and then look for components in that area that could cause this.

Let me know if you find any leaks and we can go from there. Lastly we are going to want to check for codes and see if that points us in the best direction.