These are actually three questions:
- Why does Tony not contact them? I think the movie did a very good job of explaining it, namely he is so out of sorts after the events of New York he totally does not want to even think about that bunch.
- Why do the Avengers not come for him individually? Well, given that they weren´t really tight friends to begin with and sort of drifted apart after the mission was accomplished, why would they?
- Why does SHIELD not intervene? Well, maybe it does investigate Mandarin. Tony would not know. After he got himself involved, for all SHIELD could have gone after the baddies, Tony was always ahead of them in his investigation.
My take? Fury appeared 15 min after the main fight ended, tried to debrief Tony and got the finger, and was left to interrogate