An ear infection can cause vomiting because of the inner ear and balance issues. But you usually won't see it cause a cough unless it comes with a respiratory illness. There are other causes for a cough, though, including a respiratory illness, kennel cough, or even a heart condition.
If the ear is so tender that you can't touch it, you really need to see the vet with him immediately. Ear infections can lead to bigger issues like vestibular disease and even a hematoma which takes surgery to repair.
Let me know if you need more help with this.