I'm quite surprised though. Have any of the other Doctors been as hostile to one another?
I have heard rumours to the effect that Colin Baker and Sylvester McCoy went through a somewhat strained period, but that probably had rather a lot to do with the way Baker Secundus was removed from the show.
As for companions: it is part of Fan Lore that nobody liked Matthew Waterhouse (Adric), and Lalla Ward (Romana II) was known to be "difficult". The companions of Doctor V (Peter Davison) didn't see eye-to-eye much either, but that might be because they were bored - they were badly served by the scripts.
Anthony Ainley (Master II) was a luvvie's luvvie, and apparently very intolerant of horseplay on the set, and hit it off badly with Tom Baker from the start (I think there was history there, too).