Update
I tried a little running yesterday and today. I can only run for a little bit then I have to walk to catch my breath. I figure if my joints hold up to it then I should be able to increase the running time and decrease the walking time as I go. I am not enjoying it but I'm going to continue as long as it doesn't hurt my riding.
Another thing I've learned, don't do 2 days in a row weight training the same muscle groups by accident. I misread the sheet and wound up so sore over the weekend that I could barely straighten my arms. They're a good bit better today but I'll be staying away from the weights for another day or two.
Anyhow, it's only the beginning so I figure it should get better from here.
try running slower. are you wearing a heart monitor?
if you are running, and having to walk, you are doing interval training. which isn't a bad thing.
it can start out just above a walk, as long as both feet get airborne! (otherwise it is race-walking)
i know, it sounds strange, but it worked - alternating really easy pace runs with interval and tempo runs.
there are some online calculators and strava to help figure out the HR zones.
Nice job getting out there. and it does get better.