Yes, absolutely in my opinion. I think you need to find out what your options are for work... taking sick leave for the evaluation should be fine, but if you have to go for regular appointments (even for regular therapy), you'll need a way to work that out with your manager, b/c you probably don't have enough sick leave to be gone every week (right?).

My opinion - if you talk to your manager, you do NOT have to disclose that this is for mental health treatment. Although, my guess is that when they said "no mental health days", what they meant was the way people joke about taking sick time because they mentally need a break from work, not actually time to see their psychiatrist.

A psychiatrist is a doctor. You have a doctor's appointment. If people at work ask you what it's for, you tell them... "I'm having some health problems that need to be evaluated." If they keep pressing (they shouldn't) you can tell them, "I'm not really comfortable discussing it. It's personal. Thanks though for your concern." - then switch the topic. Ask them about work, their family, sports, weather, whatever... you want to change the topic to signal that the conversation is over.

I hope you can work it out. It's really unfair that trying to get mental health care can be so difficult when you have to negotiate the time away with your workplace Because, mental health stuff is already hard enough without pressure from our jobs!

Good luck, and I hope the visit to the psychiatrist goes well for you, and you're able to arrange transportation!