Oh Melissa - your poor little girl! Abbey's poos have slowed down to three poos a day over the weekend (WOOHOO!) and her feeding has dramatically increased (by about 200mls) so am pretty happy with her!
For the sore bottom, are you using any creams? I found that initially we needed to use Zinc (with some water mixed in it - can be purchased in the baby aisle at the pharmacy) to get on top of the redness and then swapped to sudocream (or curash - depending on what was in reach!). The cream creates a barrier to help stop that burning sensation as the poo (or urine) hits the skin.
I'm not sure if you are breast feeding or formula feeding. When I posted about lactose intolerance someone said you can get tablets or something to put in EBM to remove or reduce the lactose so if you are breast feeding and the doc thinks it might be secondary lactose intolerance - you should still be able to breast feed. If she is formula fed - you can only get the lactose free formula from the Chemist unless you get soy or goats milk.
Abbey became more cheerful and back to her normal self after about a week as well. In relation to the immunisations - have you spoken to a doc or nurse about her not being able to have them due to the runs? I asked my MCHN about exclusions for immunisations and she said so long as they (bubs) dosen't have a fever they are fine to get their shots... worth checking out. Or call the Royal Children's Hospital and ask to speak to the Immunisation Nurse and ask them - they specialise in that stuff.

HTH and hope your DD continues to improve!

MG