Nope, you're totally fine. Theres an incredibly low possibility that your mom touched the tap, you touched the same part of the tap, and the few bacteria being transferred to your mouth and into your digestive system. In this (rare) case, you'd still have no problems given the fact that a high concentration of bacteria is needed to cause poisoning, since most are killed by the acidity in your stomach and small intestine.
Also that's a pretty irrational and extreme phobia - i agree with Jen, treat your anxiety, not the non existent salmonella poisoning