Winter is here and I got sick after my first “big run”

I’m doing C25K on and off but I managed to pick up from week 3 again and I was now on my last second run of week 6. I felt fine for the first two run slots but then the third one I was struggling. I got drenched in sweat and unfortunately, I got very distracted with many things and forgot to take a shower and change for a long while that day. The next day I felt my cheat tight. Then the day I was supposed to do the thirst run, I felt like I had a chest infection.

It’s been6 days since and I seem to get worse. I have been adviced to just take NAC, ibuprofen and drink lots of water and rest. I probably now need a doctor to heed my lungs and see if I have a chest infection (probably as phlegm is green :/)

Now how do I avoid getting ill like this during the winter again? The weather at the moment is mild at around 13C(55F) although that day was more like 3C/37.4F. I was wearing my long sleeve shirt, a sweater and a lightweight non-lined jacket, a band covering my ears, leather gloves (which I took off mid way), a scarf, slightly thick leggings, thick-ish socks. I get really cold and I was very cold when I went how but I wonder if I was wearing too many layers?

Is there something to do with the breathing? I did find myself breathing through my mouth often.

I have this shoes, are they good enough? At the moment I’m mostly running on paved roads.

https://www.amazon.es/dp/B01M1XUOVI/ref=asc_df_B01M1XUOVI?mcid=ef741420ec4e383f9bf5cbcbecb83984&language=pt_PT&tag=ptgogshpadsp-21&linkCode=df0&hvadid=718248761166&hvpos=&hvnetw=g&hvrand=14557720593890969250&hvpone=&hvptwo=&hvqmt=&hvdev=m&hvdvcmdl=&hvlocint=&hvlocphy=20869&hvtargid=pla-353902006725&psc=1&language=pt_PT&gad_source=1

I’m really enjoying running at the moment and the program and I really want to continue. I’m so frustrated I’m ill and haven’t been able to run for a while. It’s like my me time and I miss it :(.

Any advices very very appreciated!