Home alone IS tough. People who have never experienced it, don't realise it. And forget about trying to explain it to them. They'll always tell you they'd love to be in your position.
Loneliness is a funny thing. You can be surrounded by people and feel totally alone or you can be the only person in a place and get the same feelings. The key for me is learning to relax properly, that way, even when you are alone, you don't mind it.
It's about controlling the wandering mind i.e. when you start to think about what everyone else is doing and what you're missing out on. You worry that your social skills are suffering. You think about the past a lot, where you've been, where you could be.
What works for me (not all the time) is submerging myself in a great movie, old or new, preferably a comedy. And AT ALL COSTS avoid daytime TV! And also make plans for nights out or the weekend, so that you know the quiet moments are only temporary.
One other thing - find what it is you do well and do it. For me, I started writing. It's the most fulfilling thing I've ever done.
And always remember that no matter how much you feel it, you're not alone.