I went through the same experience except that I was on the bride's side. The moments leading up to the event was a nightmare. I couldn't even enjoy the wedding arrangements, went into depression thinking about all this because I had to read at the altar too. I kept trying to get my family to understand my situation, even at the wedding, I was a nervous wreck and just when I had the feeling that they had forgotten the speech part, I was called to deliver it (I had not planned for it at all). I delivered a speech from my heart (did the reading too), everyone appreciated it, I don't remember stuttering or blocking because I got into the flow of speaking I guess. Then after the quick but appreciated speech, I let out all the anxiety by dancing and having fun, something I wasn't able to do for months due to all the anticipatory anxiety that was building up within me. All the best! You can do it too!