Vesuvius Errupts! Did I have the right to loose my cool with woman who has been annoying me for weeks?

A bit of yes and a bit of no. Yes, she probably is jealous of the attention you get and perhaps jealous that she's not as good a student as you. Your argument was with Miss Bossyboots who sounds a real pain in the neck. You had an erruption which obviously did you good at the time - so that's not a bad thing entirely is it. Miss BB now knows she can't push you around and you aren't the shy retiring flower who can be walked over which, hitherto, she thought you were. She will therefore be a little more wary of you in the future. You did right to inform the head of department but I don't think you were right to tell the teacher she was slagging off. That sounds a little as if you were ingratiating yourself with him and stirring the pot to make him feel all warm and fuzzy towards you (a student) and dislike her(another student). He's a teacher and shouldn't take sides or have favourites. (OK, he's human and probably does - but it shouldn't be obvious enough to upset a student). OK, so Miss BB was being nasty about him and you told her off. That should have been it. The Head of Dept perhaps ought to know the whys and wherefores of a punchup in his clroom and by telling him about it you sort of covered your own back at the same time which is no bad thing because Miss BB will probably give her side of the story in due course. But I don't think you should have told the teacher concerned about what had happened in his absence. Miss BB's opinion of him is just that.....her opinion. Your opinion of him is different....again, that's your opinion. She voiced her opinion and you sat on her. She won't do it again if she's got any sense. Telling the teacher sounds like tittle-tattling to me. So yes, you shouldn't feel guilty about blowing your stack and No, you shouldn't now try to garner people onto your side to justify what you did.