Oh, dear. Sudden diarrhea can be really bad news.
First thoughts - antibiotics and sugar water are exactly what I would NOT give to a rabbit with diarrhea. Antibiotics are a known cause of diarrhea in rabbits, due to killing off the gut flora that a rabbit needs to digest its food properly. There are only a few antibiotics that are known to be safe in rabbits, giving the wrong one will do way more harm than good - might even kill the animal!
A lot of cases of "runs" in rabbits are caused by improper feeding. One of the common causes is carbohydrates, i.e, sugars and starches. A rabbit's digestive system is designed to run on a low-carbohydrate diet; feeding foods that are relatively high in sugars or starches (fruits, grains, sweeter veggies like carrots) can encourage yeasts to grow in the digestive tract, which in turn can lead to chronic looseness of the stool.
Sorry, don't mean to beat you up, but I felt that course of action needed to be stopped as soon as possible.
If I had a rabbit with diarrhea, these are things I would do:
Give it grass hay (Timothy, Orchard, Bermuda) NOT Alfalfa.
Limit pellets or even remove them.
Give the rabbit some plain, dry, rolled oats (the stuff you use to make oatmeal)
Probiotics are good to help re-establish the proper gut flora. You can give plain yogurt if that's all that's available, but I prefer animal-specific probiotics, like Bene-bac.
Diarrhea in rabbits can be caused by coccidia. It is easier to prevent than cure, though products that are at least partly effective (like sulfaquinoxaline) are available at most feed stores. Coccidia are more often a problem in young rabbits, most older rabbits are highly resistant to them.