Exhaustion/Short breath - bad recovery or something else?

Go see a cardiologist......soon.  I'm serious.....  if for no other reason then to cross that off the list of suspects.

There is basically NO recovery needed for a sprint triathlon.  There is NO WAY you are experiencing your symptoms from your race/training level.

Meh, get some cortizone.

Luckily for you, I never miss a chance to use the 3 weeks of pre-med I had in college.

Actually I did, just less than one semester......but I've been married for 25 years to the same gal and I haven't found any patterns to her reasoning that could help you. 

Still, if it was me I'd go with chlorine....  "you can either have a fat guy or a fit guy with a rash.....you choose, babe."  Have an escape plan.....always have a clear path to get out of throwing range.  She controls the narrative, so you have to control the landscape.....that's all I've learned.

Be careful, you could end up with knots on your head in addition to the rash......you can thank a physiology class I dropped for that advice.

Yes,  I would say to you should look deeper into this. 

My first thoughts when I started to read this were how hot is it where you live?  I have been dragging a feeling exhausted the past 3-4 weeks. Every year when the outside temperatures jump from 75 deg day time highs to heat indexes over 100 deg F (today's heat index is 107 deg F) I feel exhausted.   

Y&es recovery can take longer than anticipated.  My last race was a 5K and I thought I would be able to use it as a running speed workday a with a light day following the race go right back into a hard run two days out from the race and a hard ride three days out.  Well...that hard run didn't turn out so well. It turned out to be about 2/3 running and 1/3 walking.   So...races definitely require some rest time.  Light workouts at reduced volume will get you back to training a lot quicker and feeling better than taking multiple days completely off.  

My age and resting heart rate are the same as yours.  II have never seen the HR stay above 100 BPM outside of workouts though.  Has your resting heart rate been elevated too?  I don't know what could cause that.  I have had tight chests from time to time and but nothing to be concerned about.  The shortness of breath isn't a major issue for me either.  I would look deeper into that.

I know you're seeing a doctor so I am not piling on, nor intending to scare you, but those symptoms sound a lot like the ones I had when I had a pulmonary embolism (blood clot in the lung).  Good luck to you and you should see a pulmonologist as well 

And it also sounds like what I went through when my heart flipped to AFIB after years of endurance work.....and then I had a stroke 2 months later.....but I recognized it and was in the ER within 10 minutes....got all my function back within 8 hours.

This is easy stuff.......if your health seems forked up, it is...... that's why you work so hard to be healthy, to learn your body.....go see a doctor.  The worst thing that can happen is you waste a few bucks......the best thing that happens is you save your arse. 

Easy bet, yeah?  No college required.

Good job dude.....take it from an "old" guy.....don't mess with this crap.  That's how you get old, healthy, and NON-MEDICATED.  The last part is important......that's a road you don't come back from, it just goes on and on....and it's a dead end.