It sounds like you’re already doing what my first suggestion would be, which would be going to the doctor. While there, I don’t think it would hurt to ask your doctor about the possibility of exercise induced asthma (EIA). While I’m not a medical professional and I can’t say with any amount of certainty that you may have that, I know one trigger of EIA can be working out in cold, dry air. I’m not sure about the 50s and rainy that you were talking about, maybe that’s another trigger, maybe not. There are ways to deal with this and a former coach of mine runs through Wisconsin winters while dealing with EIA. If that’s what it is, there is hope.
Whatever is going on, I hope your doctor can shed some light on the subject. Best wishes and let us know what you find out.