Maybe not the belief itself (it's fine, but it can be a bit full on to effectively take on an entire religion with all the different languages, the cultural perspectives - such as a lot of Buddhists, contrary to the Western version, will eat meat/fish - and is more likely to become an 'irritation' after the initial enthusiasm).
But when you are struggling so much, a good start would be to make time for specifically Buddhist style meditations - exercise is brilliant, as you are aware, but one of the things I found helpful wasn't switching off the chatter as much as allowing it to go on and keep returning to the practices during the sessions run by the nearest Buddhist Centre.
I've always tried to push negative things away or out of my head, but after a few sessions of actual Buddhist meditation (not the 'mindfulness' or 'meditation' bollocks toshed out by people who actually don't understand it, including a counsellor), I remember one particular session. I'd become familiar with Breathing, Loving Kindness and Walking Meditation, but wasn't all that keen on the latter two - I would come out of Breathing Meditation sessions feeling happy and 'bouncy'. They were enjoyable.
We were following Mindfulness of Breathing/Anapanasati practises and I was sat on the floor in a position where the summer sunshine fell in through the side doors to the garden onto my face. I could smell the incense, the flowers adorning the Buddha state (they used the shrine room), hear a few birds over the sound of traffic and drilling and building in the city centre where they had their premises.
I was hit by the most intense feeling of sadness, terrible sadness. I wouldn't have been able to get up and leave because it would have disturbed others in the session - especially as I was aware of pins and needles starting in one leg because I hadn't quite got my position right, so would have probably fallen over with a dead leg and flattened somebody else in the process. I felt that crying would have disturbed others. Doing anything would have disturbed others. So I had to stay there and feel it. Every scrap of sadness - and it hurt. I kept breathing as much as I could. I kept trying to go back to the breathing, but the sadness and pain wasn't going away. So I sat and felt it properly for as long as the rest of the session lasted. I forgot about the pins and needles creeping into my leg, the birds, the traffic and everything else. I had to feel that sadness without disturbing anybody else.
And it started to fade. The pain lessened, I became aware of the warmth of the sunlight on my face again, the sound of a singing bowl ringing out and began to turn my attention to the feeling of my breath again.
I felt something changed in me that day. I felt stronger. Because I'd felt that pain and sadness in its entirety before it faded away in just under an hour. And the phrase 'this will pass' makes perfect sense now.
I'm definitely not a Buddhist. But I cannot overemphasise how helpful going against my instincts and seemingly doing 'nothing' but follow Buddhist practices as guided by Buddhists, rather than practitioners, counsellors, therapists or anybody offering an introductory price on ten classes, helped me.
I'm going back there soon. I can tell that I need to refresh/reset, as I've been losing track of it. Especially this last week.
In short - don't look to the belief to fix things, look into the practices as they teach them (there is no proselytising - if you catch a sniff of it, run for the hills, as that isn't Buddhism) and you might find what you need to become more at peace with yourself.