If one of your new photos really comes out well, you definitely can share it with Internet sites other than your portfolio, for instance with social networks or photography forums. However you need to take into consideration that once you share something on the Internet, you to some extent lose control over it. And there is pretty much nothing you can do about it.
Because when a photograph is popular with a large community of people, they will soon start to download and post it on other sites. And unfortunately, soon there will be even those who will claim themselves as authors of your work.
Of course, you can try to do something about it. You can upload your photo only in a small size, you can give it a watermark (normal or invisible one), you can disable saving it through a right mouse click, or you can run around from website to website and demand that your photo will either be deleted or credited as your creation. But all this is basically just a pointless tilting at windmills. Because as doctor Malcolm used to say, life finds a way.
And if that wasn't enough, you won't even get much from this type of propagation. Sure, the original sharing will lead a lot of people to your portfolio, but when the photo finds its way through the Internet, your original submission will get lost in its surfing waves and your web traffic will return back to normal leaving maybe steep, yet very narrow bump behind itself.
So if you really want to share your photos with the World, know that your authorship and recognition won't last long before your photo will change into "public property", so to speak. It's not ideal, but it's the way things go.
But if you don't want to just let your visual creation to the World, you can simply print your photo and display it in your living room. Because when the Internet decides it wants your photograph, there is nothing you can do. At best you can be glad that your work is really liked.