Hopefully you will get this sorted out ok...and you will know in the future that you really do need to take details etc. Even if there doesn't appear to be *much* or *any* damage. Its often worth taking them at the time to avoid realising you should have done later. Obviously you were a bit shaken at the time, and hindsight is a great thing, but you would have been much better to talk to the taxi driver at the time.
I havn't got a clue about what may happen now. My take on it, which may well be wrong! Is that if the damage was on the side of your car, then you were at least partly past the taxi. So even if you *shouldn't* have pulled out, you were partly past the taxi, so they should have waited for you to pass them. If he had hit the front corner of your car, then it would seem more likely that he was pulling out as you meet him (if that makes sense). Also, whilst you should have swapped details etc (and talked to him), he should have talked to you as well. So that bit seems like partly your fault and partly his. But as I say, havn't got a clue what will happen now.
What it probably is worth you doing, is trying to get it clear in your head what happened and writing it down (and drawing a diagram). Ideally this would have been better being done at the time, but even now its probably worth doing it, as the longer it goes on the more you are likely to not be able to remember what happened fully. Try and write it down clearly now, and it may help later on. Also, did you have any passengers in the car with you who saw what happened?