remember that with fighting step 1 is ALWAYS to not panic
It's ok that you are "slow" that is perfecly normal for someone new. Practice will help, your body is not used to what it has to do in order to throw punches correctly. There is a lot to keep track of with it and as you get more used to it you will speed up.
People will advise you to punch with hand weights or wrist weights, honestly I've heard as much against it as I have for it and from people whom I consider to be of equal education on the subject matter so I'll let you decide if you are interested in that particular avenue on your own, but I will say that the people I know with truely quick hands have for the most part not bothered with that.
I'll tell you one thing tho, don't throw form out the window so that you can move your hands a bit faster. Throw each blow correctly, that way when it lands it will mean something.