If you were to commit to commuting three or four days a week, you might find your insomnia decreasing. You might find your don't get sick as often.
I'm 42 years old, work as a bike mechanic standing on my feet 7 hours, have a 30 minute commute to work and 30 minute commute back home.
I'll throw out my recent riding schedule.
Thur. 3/24 no work, got in a 16-mile ride. Rode to a bike shop, picked up a frame, strapped it to a backpack, rode my bike with another bike on my back 8 miles home.
Fri 3/25 44-mile training ride.
Sat. 3/26 36 miles, short training ride, directly to work, commuted home
Sun. 3/27 no work, 60-mile training ride
Mon 3/28 30-minute commute to work, 30 minute commute home
Tue 3/29 24 miles, rode to interview for another job, commuted to work, commuted back
Wed 3/30 no ride, had a coworker give me a ride 80 miles away for a work-related training session. Commuters can be too smug cause there are times when motorized vehicles are needed.
Thur 3/31 28 miles, short training ride, directly to work, commuted home
Fri 4/1 30 minute commute to work, 30 minute commute home
Sat 4/2 51 miles training ride, work 7 hours, 30 minute commute home
Sun 4/3 30-minute commute to work, 30 minute commute home
Mon 4/4 13 miles, like you, couldn't sleep, got maybe 3 hours of sleep, commuted to work, worked for nine hours, commuted home
Today, slept like a baby for nine hours, no work, so I'll take the day off, don't do *****, sit on my butt, recover. Regular commuting by itself and in conjunction with training lets you get to know your body and it's limits. I hate to waste a sunny 80-degree days indoors, but I know it's time for a rest, and I'll reap the benefits of the rest.
Tomorrow I'll do a short training ride, work, commute home
Thurs, I have no work, so I'll get in 60 miles of training.

This isn't extreme by any means. There are tons of people older than me who work as much and ride more. There are people who work less, don't ride at all, and are constantly exhausted. My point is that in my experience, riding might increase physical fatigue, but there's a good chance your body will compensate and reward itself with quality sleep. I suspect there an element of the subconscious at work also. You put in the physical activity, you feel justified to sleep, and the sleep comes.
Try commuting five days a week for a couple of weeks as an experiment. See if positive changes come about. If not, see a doctor. I'm pretty confident even if he prescribes medication, he'll also suggest commuting on a regular basis.