I find it takes a year+ to get accustomed to the fatigue of a 2 x 30mins+ commute each day plus a normal life outside of work. (ie biking and doing stuff in free time, not lying in bed!)
Keep at it. Leave earlier. Ride slower. Take nicer, lower traffic routes. Invest in full mudguards and a rack and tough, wide tyres. Eat massive lunches. Plan for weather, especially wind.
Biking to work is brilliant. Healthy, cheap, life enriching.
Driving is an expensive luxury!
ps, biking a good distance every day will sort out your sleep problems!