I deal with a similar problem about being motivated. I have an internship doing computer science research and it drains me mentally. So after that I usually have classes and studying to do. I just keep telling myself I can do it and that in the long run school will help me to get a better job...

If your having problems sleeping this is usually related to worrying about something. Have you tried meditation for about 10-15 minutes a day for a week? Try it out meditating helps to clear my mind when I have so much going through my head.

As for studying try compartmentalization. Compartmentalize an area/location that you only use for studying and have a different one to take breaks and play around. I found I get less distracted when studying in the right location. well good luck!