Yes you are correct if you plan to compete at any level. If however you horse is a hack or field companion then you can go over but you have to be aware that your horse will not be competition "legal" until you have his course restarted. Regarding the tetanus yes the vaccine can be done as a combination with flu or seperately.
there is no lee way on the flu jab but I hear there is new evidence that the Tet jab will last 10 years the same as for humans, which is very interesting.