"Cut and lacerations of the teats can be very important and very frustrating problems to deal with. Very serious cases should be referred to your veterinarian immediatley. The most serious ones are those that penetrate the teat canal. This can be easily seen if milk is leaking from the wound (as your does' is). Mastitis may develop if infection gets into the gland through the wound. From a practical point of view, milking a goat with a cut on its teat (or udder) is difficult and time-consuming, for the ovious reason that the wound is painful. Unfortunately is the goat is to cintue to produce milk then she must be milked. This action, of course, delays the dealing of the wound. very severe cuts need to be stitched by the vet, but superficial ones may respond to the application of sticking plasters. Vets may use superflue to bring together the edges of some wounds. a serious tea wound should be considered very carefully. After treatment (sutures, plasters or just cleaning) it may be best to dry off the affected side in order to avoid a chronice open wound developing. If this course of action is followed, an antibiotic intramammary tube is inserted before drying off (discontinuing milking). the next lactation sees the affected side come back into milk. Your veterinarian will almost always prescribe a course of antibiotics, if the wound includes the teat canal. This is to safeguard against mastitis developing." from the Goatkeeper's Veterinary Handbook by Peter Dunn
After reading that, this is what I would do, move the doe to very clean conditions until the wound healed (away from herd), then:
If the cut was really bad, I'd take her tempature, then call the vet and follow their directions. (One of sign of extreme pain/distress is a grinding of teeth.)
If the cut wasn't too bad, I'd check her tempature, then check my records to make sure that her CD/T shot (tetanus) is current, put the doe on the milking stand, clean the wound with hydrogen peroxide (and a very clean white towel), then treat with a disinfectant, such as iodine. Check temp, clean & disinfect wound twice a day. If her barn conditions are good, I'd let her back with the herd, keep her from her normal area.
If the wound is not getting any better in 2 to 3 days or she developes a fever (up to 103 is acceptable), remove the kidds, clean & disinfect, and hand milk to dry her up. Also, check her temp again. I'd also give her 2cc of pencillin/100 pounds, twice a day for 7 days to combat any infection. If she was still with the herd I'd then put her in separate field with extremely clean housing (we have a hospital field for occurences like this - not big about 30' x 50').
You will now have to bottle feed the kidds, which may be a little hard at first, but they'll get it (they'll get hungry). You could feed them Mom's milk (or milk another doe) or make your own formula, see recipe below.
FYI: make sure you clean your hands really well before looking at the wound and fixing or put on sterile gloves.
The types of meds I use are:
Penicillin: Pen-aqueous sterile Penicillin G Procaine Injectable Suspension U.S.P. Injectable antibiotic in aqueous suspension 300,000 units/mL. Buy at Southern States or local Co-operative, no perscription needed.
CD/T: Clostridium Perfringens, Types C & D - Tetanus Toxoid. If she needs a shot, 2mL subcutaneously. Repeat in 21 to 28 and once annually. Antidote if reaction occures: Epinephrine. Buy both at Southern States or local Co-operative, no perscription needed.
Home made formula for goats:
1 gallon of whole cow's milk minus about 3 cups
add 1 can of evaporated whole milk
add 1 cup of whole buttermilk.
Stir.
Heat to warm then serve to kidds. I've had great success with this, and no scours!!
Hope this helps.