Well good for you for doing it! I commute similar distances and take at least a day off a week (though admittedly it's because I meet up with some friends for an mtb ride). Obviously much may depend on your own health and status (e.g. if you are 98 years old and 30 stone, perhaps commuting every day would be overdoing it a bit
Assuming you are in reasonable health and shape, I'd think commuting everyday would be possible -but of course that doesn't mean to say you should do it. My advice would be to commute when you enjoy it -don't make it a chore -unless of course you have a financial necessity there.
It happens to all of us that sooner or later that you get a bit tired. Here are some suggestions to help keep fresh and keep commuting by bike:
i. take a break now and again -or drive one way and then cycle the other.
ii. spin (SPIN) up those hills. And when I mean spin, I mean an absolute minimum cadence of around 90rpm (and some people consider that to be too slow). Don't be afraid to cycle slowly.
iii. if possible, take a different route now and again.
iv. if your shoulder is hurting you, try adjusting the height of your handlebars, or the reach to them and/or combination of saddle height. While you can rule out some positions through common sense, unfortunately this isn't always a science and you'll usually experiment with them until you find that good position for you (and even then, you'll find this ideal position is likely to change as you get fitter or age).
v. prepare the night before; don't give yourself the opportunity to give up before you start.
Hey good luck!