The term "game design" generally refers to the person who is deciding on the gameplay of a game. A game designer is a person who designs the game itself, not the art for the game. You probably want to refer to yourself as one of these instead:

game artist

game-style artist

game-style visual designer

visual designer for games

For some feedback on your examples - I like your color palette except for the light green, it's a little too moldy/swampy for me. And I would recommend a higher contrast between the two colors you are using for bone, and use more white highlights. I love the background with the fire and shadows. I think the viking badly needs eyes, he's creepy without them. The elk or moose on the life meter could use eyes too. I'm not very fond of the circles in the textures for the ground and the potion. For the potion they should have a second color to give them roundness, and for the ground, maybe triangles or lightning bolts or square facets instead. (A square facet is like the corners of your icons). Example of square faceting over a tile shape: