While there is no reason that you cannot design or implement a gallery of your own on your website you are probably far better off using a platform such as Flicker to host your photos.
One of the most difficult aspects of a "home-grown" gallery is getting the correct method of navigation and presntation of images on a wide range of screen sizes and viewing equipment. You have to accomodate everything from Smartphones through tablets to large display desktop computers.
- Flicker 🔗
Having an Gallery for your website