My animals do not handle vet trips well either, however if your cat is vomiting , and quite frequently, I would take him to the vet, he could become dehydrated and vomiting all the time indicates a medical issue.
This could be anything from Food intolerance, allergies, parasites, etc..
The bald spot on his ear may be ringworm. It can be treated with any OTC anti-fungal cream.
The vomiting is probably unrelated and could be from a number of things. If it continues and you can't identify it's cause (e.g. change in diet, eating to fast, not chewing well, etc.), then a vet visit would be in order.