Yes you can do it, if you want a big effect on a small budget in your kitchen you can paint your tiles.
1- First you have to degrease your tiles, you can use a degreaser such as formula 409 or ask anyone at Home Depot or Rona for a good tile degreaser.
2- Apply a glossy surface primer with a foam roller for a flatter surface.
An art enamel paint is ideal for tile painting, I found this one on the internet, you can find enamel paint in art stores, make sure you can use it on glass or tiles.
Kitchen before backsplash was painted
Don’t forget to test your paint on a tile before you paint the entire backsplash, if you don’t have an extra tile, try to get a sample tile very similar to yours.
Kitchen after the backsplash was painted black.
I definitely like the black tiles better than the caramel tiles, it harmonizes so much better with the grayish counter top and has a very new and dramatic look.
If you feel very artistic, once your color has dried up you can use a stencil or paint a free hand pattern on your backsplash tiles.
I would not recommend painting your shower tiles, there is a lot more humidity in a bathroom. I have never painted tiles myself, but apparently it can do wonder for a quick fix.