There's always a slight chance but as long a you washed your lip with soapy water it should be fine. A scratch from any animal can cause infection but it's not that common. If your lip starts to swell you should go to an urgi care and get some antibiotics.
As a side point, soaking a beardie doesn't do anything to keep them germ free anymore than if we worked with some contaminated substance and then just sat in some water and expected to be clean. It's soap + disinfectants that get rid of germs, not plain water. Many animals and most reptiles carry salmonella but it's not common for humans to be infected with it but it's still good to take precautions.