That feeling of passing out/throwing up is partly due to dehydration. Make sure you are drinking water, I know you said you are not doing a lot but you are working different muscles than riding a bike so those muscles take use more energy in turn making you tired faster. Your right its good to do what you can and anything helps. On my end I get to run a lot, recently I ran the army 10 miler. It was actually pretty easy, on average I run 6 or more miles three days a week. Now I don't really do too much on sat, or sun but the other two weekdays I do muscle failure. Basically push ups, sit ups or any variation of upper body/ lower body work-outs. We do a thing called 300 blasts, its sit ups or crunches and push ups, a variation of regular, wide arm and close arm. Done in increments of 25 at a time with 30 second rests inbetween, and you do anywhere from 75-100 upper body, then the same for lower body till you get to 300 of each. Its a hard start but a good work out once you do it a couple times.