It's OK to ask this question. Forums like these are the perfect place to ask potentially uncomfortable things.
This has actually been talked about before, somewhere... I'm not sure it's been talked about on these forums but I've definitely seen conversations about it on Tumblr and other social media. There are many aro folks here (myself included) who have a mental illness and/or are neurodivergent, disabled, etc. Not everyone has a mental illness - just like you said, being aro isn't a mental illness and just because you're aro or queer doesn't mean you're depressed. However, of the people who do, a small fraction (I want to say about 25%?) find that them being mentally ill interacts with their aromanticism. So you're definitely not alone in that!
I also think it's valid if the two are intertwined for you. Often, our mental health is dependent on our social lives and social health. And social health means something different to each society, each individual. In my Western context, for example, social health is equated with experiencing romance. So it's no wonder that, for some people, not having romance as a part of their lives can make them miserable. It's also possible to be mentally ill, and have that affect your social health. Often, mentally ill people shut down and shy away from people, isolating themselves. Emotions can also get either unmanageable or disappear entirely, so if you felt romantic attraction before and suddenly don't because you're mentally ill, then it could be true that being mentally ill has made it harder or impossible for your body to engage in the feelings that romance requires. Social life and emotional life are intertwined, and those things can be factors in both mental health and orientation.
As you said, identity is valid no matter what! It would be weird to say that your life experiences do not in any way influence your preferences to have certain relationships with people. Emotions are life experiences. That's my take, anyway, and that kind of fluidity of orientation is something the LGBTQ+ community has been talking about more and more lately. Orientation is probably one of those things that isn't entirely biological (being "x orientation from birth"). It's probably one of those nature + nurture things, like most human traits seem to be.
I can't make the decision about this for you, but I can tell you that it's valid to think about, and feel free to process your feelings with us.
First I would look into whether you very suddenly "became aromantic" (if I can use that phrase) and if that distressed you. Doctors use very sudden distressing changes as symptoms of disorders. Like, sudden loss of interest in things you once enjoyed, for example.
That's not necessarily a be-all end-all method, especially because flux identities exist, but it's a start.
Next, I'd try to imagine where the mental illness(es) and orientation overlap. Are they completely overlapping and seem more like the same thing? Or do they have parts that are independent from each other? What about being aro makes sense to you, and do only the parts that fit with your mental illness(es) make sense?
Hope that helps a bit. Being aro is separate from being mentally ill, but unfortunately, with stigmatization against both existing, the experiences and 'symptoms' can overlap sometimes.