As usual, Martian is spot on. However, I'll add that if you're especially concerned about someone claiming your work as their own then you're best off doing exactly as you are - keep your work away from the internet.
There are plenty of web services where you can have postcards made but you're probably better off checking out your local shops - be sure to tell them you're a local artist and maybe you'll get a discount.
Also, if you're willing to sell your work as postcards, have you considered selling it to online stock agencies? There's a lot of info to drum up but give
this site a shot (har har).