The nosebleeds could be something or could be nothing. It's best to have it checked out like you're doing to ascertain what's causing them. Many other things can cause nose bleeds, and hopefully it's nothing serious. Being winded can be treatment related, proving that is another story, and may not be, and that too should be looked into, maybe by having a complete physical, blood work-up, stress test, etc, and the shadow in the lungs explained further by his doctors.

I had nose bleeds, but weren't connected to any recurrences. I probably lost at least 75% of my strength, endurance, just from chemo in 2009, which still remains, plus I lost over 110lbs, gained 50 back, mostly which was muscle, and caused or accelerated a number of conditions ahead of its time like neuropathy, eye disease, muscle paralysis, stage 4 chronic kidney disease, chronic anemia, orthroscopic Hypotension, etc.

Good luck with everything.