Hello, and thanks for writing in. Sorry this is going on with Willy.
There are various causes for bloody diarrhea, including an infection (viral, bacterial, parasitic), HGE (hemorrhagic gastroenteritis), eating something he shouldn't have (digestible or not), a digestive organ disorder, colitis (inflamed colon), among others. Some of these conditions, such as HGE can progress quickly and dogs can go into shock. So, ideally Willy would be examined by a veterinarian as soon as possible to find the underlying cause, and for specific treatment (ER clinic, on-call veterinarian). If this is not possible, I would withhold all solid food for at least 12 hours. Water/Pedialyte is fine if there is no vomiting. After 12 hours (if the bloody diarrhea has stopped), you can offer small amounts of bland food, such as boiled hamburger and rice, or cooked chicken and rice (about 1/4 meat, and 3/4 rice). As far as giving Cephalexin...Cephalexin is not the best intestinal antibiotic, and can cause digestive upset (especially if given without food, since Willy is not eating). About 20mg/kg every 12 hours is a typical dose, but again, it may cause further digestive upset. There are much better antibiotics for intestinal problems that a veterinarian would prescribe, if appropriate.
I hope this is helpful. Please let me know if you have further questions, or if I can assist you and Willy further.