(((hugs))) from a fellow UK 'er...

Lack of decent sleep and a feeling of constant exhaustion will certainly make any depression worse.

I have similar thoughts about CBT insomuch as I feel it is very blaming, 'your thoughts are wrong, that's why you are depressed' 'if you could change your thoughts and beliefs, everything would be ok' .... er No..!
We have our core beliefs for a reason (quite often a protective factor) and no one has the right to diminish or invalidate them because they don't conform to what society deems as normal.

I too am in the UK and while like you, am glad that we have an NHS, the meagre variety of therapies available, the exceedingly long waiting lists and time limited therapy are absolutely shocking.

A lot of counsellors deal with a wide variety of issues, not just trauma. You could maybe try contacting one or two of them and asking exactly what they deal with. Another possibility is to search the Counselling Directory (just Google it), and then narrow down by area, speciality etc. Some offer lower fees or sliding scale for people on low incomes. Alternatively, MIND sometimes offer free counselling - contact your local branch.

As for feeling that you don't deserve the help because there are "others who deserve it more than you " - there is no hierarchy of need, if it's important to you, then it matters, if it's causing you problems functioning in your daily life, then you deserve to get help.

Unfortunately can relate to the issues with antidepressants and especially the side effects.
Just because you 'present well ', doesn't mean your problems are any less serious, or that you are coping any better.
I work full time and am also a carer with health issues of my own. Yes I can hold a conversation, appear well dressed, together and professional when required... But people don't see the enormous effort it takes to keep that mask in place every day. They don't see me crying my eyes out when I disappear off to the ladies, or sit in my car because I can't face an office full of people right then. They don't know how many times a day I have suicidal thoughts, they don't know the effort required just to get from one week to another.

I can't offer you any guarantees, because there are none in life. But I can offer you my support and a listening ear.

Kind thoughts
E.