Don't worry, as Zhivko pointed out - that's a normal thing for Sofia because the city is graduaally becoming a metropolis and it wasn't designed to cope with such traffic and people when it was actually planned and created. You're lucky though, because you have a metro near your neighbourhood, whereas most of the other neighbourhoods in Sofia don't have even plans for a metro.
When someone shoves you out of the way - don't  panic too, just return him/her the favour and everything will be ok. Most Bulgarians don't know the meaning of "private space", so that's like their second nature.
I have seen many traffic jams downtown, especially when I was studying at First English Language school, but one of my most notorious cases of shoving and pushing was when I had to travel to Covent Garden in London. A few seconds after the tube stopped at the station and I tryed to reach the door, a massive croud of people enclosed me like in a container and pushed me brutally forward. It was surreal. The crowd acted as one person, moved absolutely in line and I was forced to go with them until we reached one of the lifts where I was able to separate and go my way.