Can Lithium & Molybdenum in tab water cause a skin allergy?

Ever since moving to Los Angeles in 2015 I've been battling skin irritation that originated on my scalp but has moved to other areas of my body such as my eyelids, arm pits, and pelvic area. I saw a dermatologist and they were under the belief that it was an allergy. I saw an allergist and my panel came back negative, no allergies. I am convinced it has something to do with the tap water. I had bounced around with various hygiene products but found that Cleure mitigates my symptoms the best. I've tried the list below and none of them have had long term effects.

Clobetasol 0.05% Solution
Desonide 0.05% Ointment
Tacrolimus 0.1% Ointment
Ketoconazole 2% Shampoo
Cortisone Cream
Marin Soothing Hydration Cream

When I spend a stretch of time in the town I grew up in, these symptoms seem dramatically decrease but I'm never there long enough for them to go away.

I have a springwell water filter system at home, and I thought that would end my troubles, but it hasn't. I have tried a handful of other filters as well but can never get rid of whatever this is.

Update: Did some research and found out that the only two ingredients that in CA tap water that aren't in CT tap water and are not filtered out from what I have are Lithium and Molybdenum. Can these cause the skin irritation that I've described?