As far as I know, I didn’t hit any settings to change how the model looks, but for some reason it has this strange filter on it. Any help would be appreciated!
I turned it off, but the model still has that faded white texturing on it.
It actually looks fine if I press Shift+Z
EDIT: Perhaps it was Xray after all. When I clicked my mesh, not the bones the mesh, and toggled X-ray, my mesh went back to normal.
Strange. I was sure I did this before, but it didn’t work. I guess it was an update that enabled the function to work correctly (in that case, a reinstall of the version should fix it, too).
Possibly beacause you’re in weight paint mode 
Bone influence weight
And that’s the reason for the weird hatching marks on the model?
I know that the model will change a color when in weight paint mode, but I’ve never seen those markings on a model like in the first picture. I’m used to them looking like the second picture.
What hatching marks?
Could simply be a graphics driver issue. See if an update helps, but if the display doesn’t hinder the performance of what you are try to do, ie. paint weights, then I wouldn’t worry too much.