What should I do to speed recovery from a collapsed lung?

Patience. In general, there are few things you can do per se. The most important things you can do is stop smoking if you smoke. Otherwise, your thoracic surgeon will provide you with guidance specific to your condition. This will often include use of "incentive spyrometer" to promote full expansion of your lungs and "recruitment" of small air-sacs of lung. Be well.
No sneezing coughing. If you had a spontaneous pneumothorax, there is a small part of the lung that tore and is healing, for 6-8 weeks there is a slight risk of recurrence if you strain or do anything that elevates pressure in the lungs (like strenuous coughing or sneezing).