I also have sores on my bottom lip.
That is not a realistic scenario for transmission of rabies.
Also, rabies in goats is extremely rare. If you are having concerns like this frequently, it would be best to seek counseling for your fears. A concern like this is rather irrational considering that you can't get rabies from eating meat in the first place, and the extreme rarity of rabies in goats should make events like this a non-concern.
Hope you are all fine. There have been a number of cases in countries with high levels of Rabies where they got rabies from slaughtering the animal or from eating the brain of the infected animal or from cooking the infected animal and contaminating the cooked food with dirty hands and touching the nose eyes with the uncooked brain. So you have to get the bite of an animal, saliva of an infected animal in an open wound, or in your eyes nose or mouth. Also, slaughtering an infected animal and getting the saliva, or brain material on your mucous membranes or in a open wound would be the only way to get it.