When we use shower on second floor first floor bathroom smells like sewer gas. Have 3 full baths. Basement, first and second floor. All traps are filled ith water.

Hi
Sewer gas is present in all drain lines, it is just the way it is and nothing can be done to prevent it, just ways to counter it.
Your trap is attached to your drain right at the . It is a U shaped piece that holds water and prevents the gas from coming up through the drain.
If you smell gas it obviously isn't working. One reason could be a leak that allows the water to drain from the trap. If your home is not too old you more than likely have a PVC trap and they don't rust and leak but can break if something is jabbed into the drain. Another possibility is that your vent could be clogged or plugged. The vent is a pipe attached to the drain and goes up through the roof to vent out sewer gas and to allow the drain to flow freely By letting air enter the pipe.

Or could be rising damp in cellar

This could also be a partial blockage downstream from the first floor bathroom bathroom. Let me explain.
The shower discharge picks up speed going down the stack and hits a partial blockage and bounces back sending a bubble of sewer gas ahead of it. Do you hear any sounds from the traps in the first floor bath? If so then the solution would be to snake from the first floor bath. Good luck, Tom

Do not no if there is noise from first floor bath. Will check it out. Could the full bath in basement also make the smell. When I put the snake in do I put it up the vent pipe.

This could also be a partial blockage downstream from the first floor bathroom bathroom. Let me explain.
The shower discharge picks up speed going down the stack and hits a partial blockage and bounces back sending a bubble of sewer gas ahead of it. Do you hear any sounds from the traps in the first floor bath? If so then the solution would be to snake from the first floor bath. Good luck, Tom

Could problem be starting in basement and if so do I snake up the stack

do i snake up the stack no, you do not snake the stack. The solution would be to pull the toilet that bubbles and snake from there. Good luck, Tom