Its due to the injury near the ear. Mygoat is correct.
Our ACD had a similar injury last summer. No bite. Injury unknown. He just showed up one morning with his right ear swollen double.
We did a couple of drainings on it to no avail. It kept refilling with fluid. Finally we took him to the vet. Three procedures later he came home with his ear sandwiched between two pieces of plastic to keep it from refilling again. It healed but he has a little 'crinkle' in his ear from the original injury. This is what he wound up looking like with the 'splint' on his ear.
I'd like to say that it will heal on it's own but that's unlikely to happen without the ear becoming deformed. What has happened is that the skin has separated from the cartilage. The little goat is probably shaking his head, exacerbating the swelling. His ear hurts. Keep it clean. Use triple antibiotic ointment on it and watch him for signs of systemic infection from the bite until you can get him to a vet. I don't know about your area but this wasn't an 'expensive' fix at all.
Please do not inject anything into his ear. While draining the swelling will give him relief, you are not a vet and once again, mygoat is right. You could inadvertently damage the ear so he winds up looking like a prize fighter.
The dog's owner should be held liable for any treatment costs for your little goat. I'd definitely file a police report and be talking to a lawyer if he isn't willing to be responsible. That dog is a menace. If it bit a goat, it is only a matter of time before it bites a human.