As a vet and long-time lamber, my heart goes out to you, I know watery mouth is a horrible thing to deal with.
If it is watery mouth (which it sounds quite like to me), the E.coli and similar bacteria that are responsible feed off the milk and multiply.
If you can just feed electrolyte/glucose solutions for 24-48 hours (Liquid life-aid do a good one, but there are a lot available) and withhold milk it might help her out.
If you can feed the fluids warm (body temperature for a sheep is about 39-39.5C, so anything up to 40C is comfortable to drink/be tubed), it'll help keep her from getting cold, as you have said her temperature is low already.
Lots of TLC, regular feeding of electrolytes and the antibiotics will help, and as she's a bit older than your typical newborn with watery mouth, hopefully her immune system will be better ready to fight it off.
Everyone uses a different prevention method, and it really depends on your farm what is best. I have known a lot of farms that have used the oral pumps previously, and after a while start to get a problem, which may be resistant bacteria. An intramuscular injection of Alamycin is also a very good option, and if this is the only lamb, or there are not many affected, I wouldn't jump ship and change to something else too quickly, it may just be that the particular bug she has is not responding, but you have prevented a lot of bugs getting into all the others. If you do have a problem with similar sorts of disease this year, it might be worth chatting to your own vet, and considering an alternative prevention next year.
Anyway, I wish you all the best with the lamb, and hope that some of this might be of help

Suzanne