I followed your advice when you stated go to Image>Image Size... This will adjust the quality of the image, allowing you to adjust the pixel dimensions and keep the full image.
I then click on 'custom' to customize the width and the height of my image.
Every time I change the number representing the width, the number representing the height automatically changes and vice versa.
How do I change the number of the width without the number of the height changing automatically and vice versa?
You click on the "chain link" between the two values to turn it off, but if you change one and not the other, you warp your image.
The link is there to keep the perspective ratio.
If your question is answered, don't forget to mark it as answered.
Gener7 has given you a good answer. If what you want to do is to change one dimension, but NOT the other, you might want to use "Canvas Size" instead. "Canvas Size" will allow you to crop an image in one or both dimensions and for me is easier to use than the Cropping Tool.
Please understand that if you make an image LARGER in any one dimension, it will fill the new pixels with the "background" color. I like Canvas Size because you can specify the sizes in Pixels, Inches, or Percent. And you can even specify "relative" sizes. So, for example if you want to make your image 20 pixels shorter, you can check the "Relative" box, the units to "Pixels" and set the Height box to "-20". You can select which edges get cropped, too, using the "Anchor".