Not wanting to interrupt and getting wound-up.

If I get into a converstaion with somebody and halfway through the conversation, I realise that I need to be doing something else, I find it really difficult to say to them 'sorry to interrupt, but I really have to go and do this now'. I let them carry on talking but inside, I begin to get stressed out and start scratching myself (usually my arm or face) quite hard so that a visible red marks are left.
I eventually stop this when I hear a suitable break in what they are saying, then I will say, 'ok, I have to go now, chat later' etc.

I get so wound up with myself and with the other person, even though it may be a completely normal, happy conversation.
I then get annoyed with them for talking and with myself for not being able to interrupt, so the scratching starts.
This only happens say, once every couple of weeks.
I am wondering, does anyone else experience this?
I don't like to interrupt because if it was the other way round, I would be embarassed if somebody suddenly cut me off mid-flow.
Help!