You're bathing in toxic tap water. You absorb 10 times more fluoride and chlorine in the shower than you would from drinking a glass of tap water because the heat opens your pores and you soak in the water, not to mention the chlorine vapors evaporating and you breathing them in.
I would invest in a shower filter that filters chorine, chloramine, VOCs and heavy metals.
Unfortunately I haven't found one that also filters fluoride, but the rest of those can be filtered by spending 50 bucks or so.