Starting your own business is the most secure way to work from home, or your own personal office to work from, but to be honest it wont help you overcomce the fear of working with others, even though you feel that you cant interact properly with people, thats not the case unless your mouth has been stitched together and your a vegetable whick your not, if that happened then sign language or writing down a message on a white board would be an alternative, its true though, people will put up with alot and just because you think your a clux at talking to people doesnt mean there wont be people who may enjoy your company anyway, there are good folk out there who arnt that prejudice, you just havent realised this yet, more outgoing people are the same as you only they can express opinions more often with confidence, but thats about it, they eat breakfast lunch & dinner, have crap days, just like you do, but that doesnt make you alien to them or visa versa
my point is that, you need to challenge the anxiety as often as possible, sure it'll be painful but its not beyond you at all, try not to limit yourself to this option as you may find data entry alone boring after while, and you end up doing it all on your own where there are people in the industry who may help you if your employed at a company with other colleagues.
In the end its your decision, as long as you pursue it for the the right reasons.
Often artists, free lancers work from home for an agency but thats after years of working for a company in a teamwork role developing a worthy folio.