The most important thing is to see a doctor not "sometime," but actually book an appointment this week. Because two months of constant shortness of breath isn't normal even for long COVID, and you need to rule out complications like heart problems, blood clots, or pneumonia. The doctor might send you for a CT scan, EKG, blood tests - that'll take a couple of weeks and give you a clear picture.
What you're describing does sound like long COVID. It's kind of like the virus damaged your blood vessel cells, your muscles got depleted during the illness, and your blood microcirculation is messed up. Your body takes longer to recover than it seems like it should. Here's a practical tip that people usually miss: try graded physical activity at a pace way below what you're used to. Obviously not running, but a light 30-minute walk at an easy pace, then rest for a day or two. Then repeat. For a lot of people, careful muscle and endurance recovery helps way more than complete rest.
Talk to your doctor about vitamins and minerals too (iron, magnesium, B12 are often low after COVID), breathing exercises, and maybe a rehabilitation program. Recovery can take months but it does improve with the right approach. The main thing is not to put off seeing a doctor.