The oversized tires could be placing a burden on worn front suspension parts, like worn ball joints or tie-rod ends. Also, if large tires are even the slightest bit unbalanced, this may cause the shimmy too. But, you said the shimmy happens when you brake. This may be indicitive of a warped rotor, which may not have been noticiable with the standard tires but now it may be projected ten-fold with larger tires. Bring the car to a shop that does both brakes and suspension repair and have it checked. A good tire shop will do both types of repair.