Mental illness is not made up, nor is mental wellness. There are problematic aspects of the mental health field, but there are problematic features of every field.
Physical diseases have been around for 100000+ years too, part of life, but we don't say there's no such thing as health or illness.
I agree that the the diagnostic categories in things like the DSM are probably imperfect, and many aren't "real" but there are many in the area of mental health sciences who would agree with that. But that doesn't mean mental illness or wellness aren't real, any more than mismodeling bacterial disease in the 1800s didn't mean they didn't exist.
Part of the problem is that people want to project concepts from things like cardiology or virology or oncology onto behavioral health and it doesn't quite work the same. But that doesn't mean it's not real.
As for therapy, there are decades of randomized controlled trials with all sorts of controls that show efficacy of treatment: various types of treatment and behavioral controls, waitlist controls, pharmacological controls, and pharmacological placebo controls. It works on average, just like everything else. Not perfectly not all the time, but on average it works. We can get into arguments about why it works, and I think there are serious issues about what the "active effective components" of therapy are (I don't think they're what e.g., CBT theorists think it is) but that's a different issue.
This is a good overview of my perspective on things; note that it assumes therapy is effective, because there's so much evidence at this point that it is, but asserts that no one really knows why:
https://doi.org/10.1146/annurev-clinpsy-050718-095424