No, No, No.
Never change resolution of a photo unless the proportions are constrained, kept the same, etc.
In other words, don't ever ever ever up the resolution of an image unless the size or width/pixels stays the same.
If you have a 72 dpi image from the web, and you want to print it, in scale, don't resize it to 300 dpi unless the size or proportions will be constrained.
If the original image is say, 72 dpi, 12" wide, at a size of 300K, and you change the dpi to 300, keeping the constraints on, the size of the image should stay the same, i.e.: 300k
Now, if you want to make the image smaller, you can always go down, you just can't go up.
You can go to a 300 dpi image at 2" wide, which will probably give you a size of 150K, and will be fine.
Make sense?
.