First of all, get better soon!
Secondly, it may not be due to the snakes. You're far more likely to get salmonella from something you ate either at home or in a restaurant (or even by touching certain fruits at the grocery store), especially if you eat a lot of uncooked vegetable foods like salad or guacamole. Unless the doctor did a culture and found that it was something specific to reptiles, I feel like that may be more likely since you use appropriate hygiene around them.
I don't think they all necessarily carry it, but I'm not sure what the exact rates are. I remember seeing somewhere where turtles were the worst reptiles to transmit it, but I'm not sure if that's because they're more likely to have it or because people are more likely to touch a turtle and not think about immediately sanitizing their hands.
I've had reptiles for about 16 years now and never came down with any sort of illness from it, and I certainly wasn't on top of hygiene practices when I was 12, so I'd say it's typically pretty difficult to get salmonella from them as a general rule.