In addition to ddawn's good advice, I'd like to add the following:
Laying hints:
-All of your layers should be on a diet of 16 to 20% laying mash or pellets for at least 90% of their over all diet.
-Always offer oyster shell free-choice to layers. As laying mash is made for the average hen who needs 6:1 calcium to phos, but some hens need as much as 15:1 cal/phos, always offer free-choice prepared oyster shells. I prefer the crushed shells over the pelleted. This should be fed in addition to any grit as it's too easily dissolved to act as grit. Do not feed egg shells; they're simply not as bioavailable a souce of calcium. Feed separate from the feed. I feed mine in a container with the granite grit. (Last time I bought a two-dish cat feeding plastic bowl at the dollar store - works great, doesn't shift, doesn't get knocked over.)
-Feeding new layers plain yogurt weekly not only increases their calcium, but gives them some vitamin D which is essential for calcium absorbtion. You get the added benefit of boosting their beneficial bacteria, which is wonderful as the first weeks of laying are stressful and can predispose a bird to illness.
-Make sure that you don't feed excessive grains. Grains are high in phosphorus and though phosphorus is needed for calcium absorbtion, too much will make a hen cease to put calcium into egg shells - and eventually lead a bird to leach the calcium from their own bones to make up for the excess phosphorus.
If you hadn't mentioned the very loose droppings mixed with blood, I'd almost think that a new layer (as you said you were surprised to see an egg) might have simply bled as the cloaca hadn't yet had an egg pass through it. Sometimes fissues in the cloaca can bleed into the droppings making it appear as if there's blood in the droppings. However, the diarrhea make me at least suspect cocciodiosis although it's more uncommon for older birds in dry conditions. I'd second ddawn's recommendations of determining whether the blood was in the droppings, or possibly from the vent. DO examine all droppings very carefully. If you know which hen, isolate her for a day. Do the yogurt and oatmeal in the mean time as they'll help in any case and might clear up the diarrhea at least.
Diarrhea treatment:
Using a little plain yogurt daily for birds with any digestive symptoms can replace the beneficial bacteria that help them fight diarrhea (as well as fighting opportunistic pathogens like bad bacteria and yeast/fungus). So give them a little treat. "Hiding" it in cooked oatmeal additionally can sooth their gut (oatmeal), as well as make the good bacteria happy by providing them food (oatmeal fiber). Cook it more dry than normal, use the yogurt (1 teaspoon or tablespoon per hen) to make it a more normal consistency. Plus what birds don't like oatmeal?
Avoid higher proteins during coccidiosis. Normally I'd say "use boiled eggs to get them to eat yogurt" but during coccidiosis, no. If you use it to keep your healthy hens healthier - yes!
I'd second ddawn's recommendations of Corid as it treats 9/9 cocci species. If you simply cannot find it, you could use Sulmet but you'd have to discard eggs and it's also an antibiotic, more harsh on the system. However bloody diarrhea is serious. I'd use the product I can find within 2 days.
best of luck, and please respond here with any updates as we'll be here watching for word from you.
