Been getting pneumonia a few times in past 6 month or so and naturally worried. which is better: infectious disease specialist or pulmonologist?

Either or both!: Either one would be helpful, both may be wise. And second opinions are great anyway. Get too different takes on your problem, ask plenty of questions, and take notes for later pondering. Your primary care doc can recommend trustworthy docs and may have an opinion on which you should see first. That is part of the job of your PCP, to send you to the next best level of care for complex problems