STDP:
Is she allowing the fawns to nurse? It could be mastitis or maybe when run thru the chute she may have bruised her udder. I am going from dairy experience,I would run her back thru the chute or tranq her. Get a small screen or cheese cloth and milk each of her quarters. If bruised you will get bloody looking fluid or straight blood. If this is the case about all you can do is let it go that I know of.
If it is mastitis it will have chunks like cottage cheese or stringy slime. If it is mastitis you can treat with goat mastitis treatment, which is a antibiotic you put into each teat. Looking at your picture I doubt it is mastitis, because the udder would not swell up that quick. I hope someone with more deer experience will reply also
Denny Pell
MapleHill Whitetails