NQ but RMN.
Firstly, I'm sorry you're experiencing these difficulties, both in terms of your practice and its effects on you, and in receiving adequate support.
In my experience clinical supervision is (and should be) offered to practitioners in all areas of mental health/
counselling, and for many disciplines is mandatory. Given that you're working directly with clients with psychological needs I'd have hoped this would be reason enough to provide it. I do question though whether it's clinical supervision you're actually looking for; often this is used as a means to develop and bolster your practice, by reflection and drawing on another clinician's experience, and as far as that goes it sounds like it will be useful in exploring ways for your job to effect you less, and for you to feel (and perhaps be) more effective in your role. I'm assuming you're working outside of a mental health Trust per-se? If your employer can't provide anything "in house" I wonder if it's worth looking for a supervisor in a neighbouring mental health Trust. Otherwise it can be provided by (for example) a Psychologist or therapist on a paid basis. I'd certainly argue that given your job role there is a need, and there's a lot of literature supporting this. It may also be argued that this constitutes a "reasonable adjustment" to allow you to do your job, assuming that you fall under the remit of the Equalities Act.
On the other side, I do wonder if a more counselling based approach may be useful for you, and often this can be sought via occupational health.
I hope that's helpful, and you find the right support for you.
29th March 2022