Do I need to use silicon seal (caulk) and a sealant strip around the base of my shower
The sealant strip is supposed to cope with some movement of the shower (or bath) by being flexible.

However, what usually happens is that it's not quite flexible enough or loses it's flexibility with age so water starts seeping around it. This is when caulk or other sealants are added on top.

If you can get a good seal with the caulk (which you appear to have done) then you don't need to add the strip.