When I was young and cared more about my career than was healthy I practically worked myself to a breakdown which doesn't sound too dissimilar to yourself. I went down the GP route as, rightly or wrongly, I didn't want to have the conversation with co-workers or my manager at the time for the unfounded fear of how I'd be perceived. GP was great and they can be quite understanding of professional pressures on how the fit for work note is presented if you have any specific concerns. Go speak to the GP if you think a break would do you good. I started with a few weeks but ended up having three months off in total as it took that long to get back on my feet. For me being signed off put me in the mindset that I needed to get myself on the mend and it helped me be more proactive in doing things that helped my wellbeing (it also conicided with the GTA5 release but that was pure, but happy coincidence).
All the best.