story-identification: fantasy story with physically weak protagonist that took place after nuclear winter

I started reading this book when I was in either elementary school or middle school (anywhere from like 2004-2011) that I recall was too boring for me then but that I’m very interested in remembering now. Unfortunately I don’t remember much about the book except these key details:

• I think it was written in the first person
• The main character was a boy/young man who was physically weak, too weak to be a knight, but was actually very skilled in military strategy
• He might have had asthma?
• The fantasy world they lived in was cold because it was actually Earth in the aftermath of a nuclear winter – this knowledge was not revealed at the end but was part of the book’s exposition and not considered that big of a deal
• The main character might have been attending some sort of knighthood school or something in the beginning
• There may not have been any magic in this setting (but also there might have been and I don’t remember)
• Eventually he has to go out on some sort of quest, but he is insecure about his poor physical prowess
• He had some sort of female friend who supported him
• The book cover was some sort of landscape that was mostly green and grey
• I don’t think it was high fantasy – as far as I know, humans were the only race present

Sorry this is so incredibly vague! I’ve been racking my brain about this for hours now and can’t seem to find it anywhere.