Exhaustion/short breath. Bad recovery?

Hello all,newbie looking for some guidance here.Please bear with me for a few paragraphs.

INTRODUCTION. I am a beginner male in my early 40’s, training quite regularly around 5-7 hours a week for the past three months (have always been moderately training for other sports before that, never a smoker/couch potato). Have been running quite a bit in the past. My best on half marathon is 1h46; on 5k 24’.

I successfully competed in a sprint Tri (my first ever) about three weeks ago, 1h27. Nothing spectacular but getting in the groove. After the race I was exhausted, which sort of felt normal.

RECOVERY AND EXHAUSTION. Right after that race I basically did not train for a week, trying to recover, but also had to face a tough work/travel schedule for a business trip; 4 days after the race I took off - 6 flights over the following 4 days, plenty of jetlag. I have felt exhausted ever since.

Upon my return home from the business trip I tried to sleep, eat well, recover. But no success. For 2 days, my pulse would not go below 100 (my regular rest HR has been around 48 for the last couple months). Took a couple pain relief pills. The pulse ultimately went down; but I continued to feel a sense of compression on my lungs, uneasy breathing even at rest, and in the following days, when running I would almost immediately run out of breath, could not run beyond a few hundred yards.

Last weekend (so three weeks after the sprint), I had planned to compete in a Olympic tri, my first ever such distance. Was unsure as to whether it made any sense given my poor shape but ultimately decided to take it easy and give it a go. The sense of compression on my lungs had gone, at least at rest. So I competed: swam and biked slowly (35 minutes for the 1.5k run and 1h25 for the 40k bike), but no real problem. In the running section my energy level collapsed, and in particular I would constantly run out of breath. Ended up completing the race only thanks to some walking and vey slow jogging (took me 1h10 to run the 10k).

Note that during and after the race was very careful with nutrition and hydration; took 5 gels between the bike and running; drank plenty, including minerals-enhanced water. The day was very hot, around 90, which definitely impacted on my performance.

The day following the race (that is yesterday) I tried jogging just to shake my legs. I would run out of breath after 10/20 yards, no energy, impossible even to jog for more than a few steps.

CONCLUSIONS. So: my reading is, I never really recovered properly from the Sprint and my energy level is still affected from that. That kind of explains it, but I am still puzzled by the difficulty in breathing. Is this a sensible theory or should I look deeper into this? Any advice on what to do now/next time around (beyond the obvious I should have planned and executed a better recovery from the sprint?) or comment much appreciated!

Thank you!

Pon