You could buy private web space. Better yet, find a friend who has a web site and he can provide you with a page on the site.
But lei's say that is not right for you. You have media skills, not HTML skills. There are places that let people have free space for artists to show their stuff.
Facebook
Flicker <-- this might be best for you.
WordPress
Photo bucket
...to name a few. Other:
Zooomr
Picasa Web Albums
Photoshop Express
There are more, just can't remember. And yes, you can use Facebook for photo sharing. Depends on your skill level. But photo bucket is very simple.