Probably just stepped on a thorn or nail or something. At such a young age is seems unlikely it is foot rot, though you did show the hoof itself. That is where foot rot will form. I have had bumble foot on lambs of that age a few times, but that is rare and will be very hot to the touch, and mine were always a bit higher on the leg.
Any of the three have the same treatment if you chose to do it yourself. 5 cc's of LA-200 which you can get at any Tractor Supply or other Livestock Store, and inject subcutaneously under the skin. Do this on day one, wait a day, then give a second shot on the third day. LA-200 is a strong, long lasting antibiotic which is why there is a wait of a day.
Another trick I use for foot rot and injured hooves is to mix tetracycline powder (sold at Tractor Supply as well) and mix it heavily in a water bottle. If you are talented, you can get them to stand in the bottle and get the antibiotic to soak into their hoof/wound, but I am not that good. Typically I take a small drill bit (1/8th or so) drill a hole in the cap of a 20 ounce water bottle, and then spray the antibiotic directly on their affected hoof. It works well. I have a lot of sheep so I have a foot bath, but for individual seep with hoof problems, this is what i do. In fact I got a sheep now with hoof issues so don't feel alone.