The big risks of salmonella is with reptiles, not fish. If you wash your hands with soap after being in the tank, everything should be fine.
If it's of any help to you, please tell your parents that all 3 of my children were raised doing aquarium maintenance, and it has never been an issue. My 10 yr old daugher now has her own tank and her own betta in a bowl, meaning she tanks care of them completely. I don't worry about glass because her tank is acrylic, and she's careful with the bowl.
I have found that letting my kids do the tank maintenance they learn more, including how to appreciate life. I have been putting my hands into fish tanks daily for more than 15 years, with and without cuts and other injuries. It has never made me sick. I can find no logical reason to not let a child do their own maintenance. With medications, that is another story, and best left to an adult. Some people have allergies to some forms of fish medications, and that can mean anything from a mild rash or itching to severe burning of the skin and other illnesses. But, if a tank is healthy and well cared for, fish carefully selected, properly quarantined... there is usually little need for medications to be used. I have a tank that has been running for almost 10 yrs now, and has never once had medications put into it. It's still thriving with the original fish.