Tinnitus is the medical term for ringing in the ears. Its causes vary greatly and the common one is continued exposure to very loud music. Other causes are like ear infections, stress, as one of the side effects of taking too much aspirin or age related. The electric toothbrush can not cause tinnitus but if it's so loud, then t might cause. In fact the electric toothbrush can be used to cure tinnitus; take an electric toothbrush and use it to massage the area behind your ears. You might want to put something soft around the toothbrush.
By any chance do you have dental works involving different kinds of metal? This has been known to set up galvanic current and create a kind of audible "static" or "white noise". There have even been people that have picked up radio broadcasts in their heads! This is very rare but proven to be real.