I need some help identifying my bottom bracket. One of the bearings is in a very bad shape and needs to be replaced. Bottom bracket photos
It appears to be a standard square drive sealed cartridge type bottom bracket. It looks as if it came apart. Normally the bearings are not removed from the shaft but are removed and replaced as an assembly. If you measure the width of the frame where the bearings were removed you should measure 67mm or 73mm. Measure the length of the square driveshaft. The length will vary depending on the bike type, drive train etc. The other option is English or Italian thread. Most likely it is English but you can't tell from the photos. The options are to look on-line for a bottom bracket that matches your measurements or bring all the pieces to your LBS (local bike shop) and have them measure and match to something in your price range.
It's a generic BB. The 3P code on the spindle is a clue to the size.
Sealed cartridge BBs are ridden until they fail (ie bearing disintegrates, like in your case) at which point you buy a new BB unit. You can try just getting the bearing (but IME it can be a frustrating endeavour). There should be numbers on the bearing face jot those down and visit a parts/auto shop or have our LBS order (if they can). Most parts/auto shops will have a compatibility chart of bearings between brands.
For example here's a link showing how to identify an SKF bearing http://www.skf.com/group/products/bearings-units-housings/super-precision-bearings/double_direction_acthbb/marking-on-bearings/index.html
If you can't find a compatible bearing you have no option but to buy a new BB unit.