Hi Spectre88 and welcome!
I used to be exactly the same at work. I would explode over a phone ringing. I never felt lonely or depressed, but I was so angry and irritated all the time. I got to the point where I wanted to stab someone with a red pen. I realised that it was an unhealthy situation, but wrote it off to job stress and changed jobs. Two months into my new job I had a full breakdown and fell so deep into depression that I can't seem to get out again.
I have learned that depression is not always sadness, the sadness can manifest as anger. And for me, when I took the anger away the sadness came. Dragging along with it all the feelings of self-hate and loneliness that I buried so deep for so many years.
To answer your question, no you are not alone. Paying for therapy is also very hard for me, so I found a counselor willing to help me after hours for free. I also received some meds to help balance everything in my brain again (waiting for them to work). But I would say you need to see someone because there are some feelings you need help handling.
I hope you feel better soon! And I hope my rambling helped a little bit.