Hello and welcome to Just Answer
It is very possible that he has an ear infection
based on what you describe. Typically when there is wobbling or falling in conjunction with head shaking the ears
are involved. This can often be the result of a middle or inner ear infection that affects the proper functioning of the vestibular system (responsible for coordination and balance), or even rarely a polyp. Unfortunately it can be difficult to successfully treat this at home. A thorough examination of the ear is required to determine the cause of the condition and verify that the ear drums are intact, i.e., not ruptured (often happens in bad cases) before treatment begins to prevent potentially permanent damage. If the ear drums are intact many medicines can be used to combat the infection which may be caused by bacteria, a yeast or even ear mites. (I attached a few links with more information)
If you stick a corner of a cloth in the outer ear canal and try to clean it and you get some dark waxy stuff with white specks in it, it might be ear mites. If you have a very strong magnifying glass you might ever seen them. If you find ear mites you can put a few drops of mineral oil in each ear and squish it around by massaging the bulb on the back of her ear. After ten minutes or so you can wash it out with a mixture of 50/50 vinegar and water. If it is mites Eradimite Ear Mite Treatment is what I prefer to use, or something like it. There are other treatments available at most pet stores, or online.
If it is a bacterial or yeast infection I prefer using Otomax or MalOtic ear drops, unfortunately these are prescription medicines. These types of infections often extend into the inner ear.
I hope this helps