In this day and age, I believe internet relationships are just as real and acceptable as 'in person' ones are. I've met quite a few people online through various message boards or websites that I've had the pleasure of meeting in real life and we've been friends for years. Some I've met were less than stellar.
I think it's absolutely normal to have feelings for someone you haven't met in person but spend a lot of time with online. Of course, you have to be careful and safe in a virtual or real life situation. For the most part, when you spend time with someone online, you do get to know them in a more comfortable way and a lot of times it is without that uncomfortable or awkward way we have sometimes in person. Your main communication IS communication so that's kind of nice. The downside is not being able to see their reactions and hear the tone of their comments. All kinds of pros and cons but it's just as real.
And of course, as other people have said, the internet relationship can't be your entire life. If you're hiding out from the outside world, it may be a problem. Good luck and be safe!