The short answer is:  YES!  According to the Center for Disease Control, “Even after being visibly rinsed clean, toothbrushes can remain contaminated with potentially pathogenic organisms.” Yuck!  Here are some tips to get (and keep) your toothbrush clean. Keep Your Toothbrush in Tip-Top Shape
Clean your hands with soap and water before and after touching your toothbrush. Wash your toothbrush after every use. Use your thumb to press against the bristles and allow the water to wash away food particles for at least 10 seconds. Disinfect your toothbrush by soaking it in some antibacterial mouthwash that contains alcohol for 10 minutes after brushing. Replace your toothbrush at the first signs of bent bristles. Replace your toothbrush after you’ve been sick. Buy a new toothbrush every 3-4 months.