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Did the vet check her teeth? This sounds like a tooth or pouch issue. It is common for an overgrown or maloccluded tooth to cause constant drooling which wets the chin and causes the fur loss. It can also happen if she chews the bottle spout due to the wetness. The teeth, if overgrown or if there is an abscess or lump in the pouch can cause issues with the tear ducts so they don't drain tears and cause the eyes to get irritated. The red discharge is not blood but a substance as cyphen said called porphyrin which is secreted from the back of the eye due to infection or irritation.
Check around the pouches for any lumps. Does she seem to have anything in there all the time?
Often eyes are a symptom of something amiss elsewhere and not in the eyes alone so important to have everything checked out. I hope she gets better soon but I'd have her rechecked especially the mouth.