Handling or eating cooked goat meat does not transmit rabies. Rabies spreads through the saliva of an infected animal via a bite, scratch or a lick on broken skin - not through meat, and cooking kills the virus anyway. Your mouth burn is a simple thermal ulcer from hot food and it heals in a week on its own. So this is doubt, not risk - no vaccine needed here.
Next Steps
Cold water rinses, avoid hot/spicy food and use a mild oral gel for 3-4 days. If the ulcer is still there after 2 weeks, or you had an actual bite/scratch from any animal, book a consult with me on Practo and we will decide about vaccine properly.