I am sorry to hear about your squirrel.
Signs of worsening and improvement.... The coughing sign can be unpredictable. Sometimes it indicates improvement and sometimes worsening so it is worth monitoring but should not be the only sign to monitor. The main signs are going to be overall appearance and attitude. His alertness, appetite, activity and hair coat condition will all mirror his internal health. If his pneumonia is worsening, then his demeanor, appetite and activity will worsen. The other abilities to monitor would be those at your veterinarian: repeat radiographs, blood work, pulse oximeter, etc...
A few notes: squirrels have a high metabolism. It is important to make sure that he is eating and drinking regularly. If he is not, then regular supplementing and nursing care every few hours will greatly improve his chances. Also does your veterinarian or other local veterinarian have a nebulizer? Nebulizers are basically vaporizers that also have antibiotics in their humidification. The treatments are usually fairly inexpensive and can noticeably help.
Best of luck.