How can I quickly improve the resolution of my photo?

Well, you can try Photoshop alternatives for giving the effect which you want to give to your image. They are also good as Photoshop is in terms of image editing. One good image editor is GIMP which has similar tools just like Adobe Photoshop and is capable of performing any kind of image editing task. It is free and can be downloaded from its official site. Here is a link:

http://www.gimp.org/

GIMP Tutorials Link:

http://www.gimp.org/tutorials/

GIMP Manual Link:

http://docs.gimp.org/2.8/en/

Other good alternative to Photoshop is Pixlr. It is free online image editor. Although it has similar features like Photoshop but is less powerful. Here is a link for it:

https://pixlr.com/

Pixlr is also capable of doing most of the complex image editing work.