This is a misconception many people make. Sushi does not refer to raw fish, the term used for raw fish is sashimi. Sushi is actually reference to the rice. Anything served on a ball of rice (nigiri sushi), rolled in rice (maki sushi), or in a small nori cone filled with rice (temaki sushi) is sushi; they have a sweet egg omelet, called tamago, served on rice that many people who have a fear raw food eat.
Others you may try are: ebi (shrimp), masago (smelt roe), tobiko (flying fish roe), anago (conger eel), tako (octopus), kani (crab), surimi (imitation crab). These are all cooked and are good things to try if you are worried about raw items.......maybe you can work your way to some toro (fatty tuna) which is one of my favorites!!!