"My youngest daughter , age 9 and an amazing trooper who had no problem keeping up with any of us started having situations of coughing that would not stop, "chest discomfort" and I'd say difficulty breathing.
I remember both vaguely and clearly the first time I had what turned into asthmatic hayfever attacks. I think I was a little younger, maybe six or seven. We had been playing in high grassland near the river, and I came down with a strange cough mixed with breathing problems. Those breathing problems were more in the background that time, but later they would become the main concern.
Looking back, I regret to say that my doctors were not the best. They did the same tests over and over, and never gave me medication that worked. I taught myself to keep calm and relax, but that took until I was in my late teens (and even then it did not always work). I don't think a young child can manage that. Like the OP's daughter, I only wanted to join in the fun and be like the rest. Unfortunately, forcing myself only made my breathing problems worse.
One thing that was very good for me during the hayfever season was being near the ocean. The wind from the seas, the fresh air would unclog my lungs within one day.
The first big improvement was called Ventolin. A small inhaler, the size of a cigarette lighter. I'd inhale, hold my breath and ...gone! The second breakthrough came about decade ago. The flu had hit my lungs, and my GP prescribed a 'disk'. It worked like a miracle. When I had finished the prescription, he urged that I'd continue to use it, to protect my lungs. The hayfever season came and went, I barely noticed it and I have not had a hayfever attack since. *knocks on wood*
IMO what happened to your daughter was very real, and you reacted well. Fortunately you have ample time before your next Camino to have her tested and put her on medication.