+1 for Stephpd, above! Trial lawyer and former prosecutor, here. FWIW, here's adding my humble opinion ("opinion" = "best guess at the time"):
For all but the most seasoned, adrenaline dump may be accompanied by confusion, shock, and more often than we might think, a temporary but strong state of denial. All come at the same time. It is hard to get your head around what happened, at best. People can innocently end up giving confused or seemingly conflicting information, and sometimes may say what they wish had happened, instead of what happened.
Even while your mind is racing, you might sometimes appear quiet and subdued to those around you. Later, in court, they might interpret this as indicating you were in a calm and rational state of mind. Also, some statements which might help you in criminal procedings can fry you in the civil trial, and maybe vice versa.
Special note: Please (!) don't underestimate the possibility of accidentally saying something that later seems conflicting or inaccurate, and PLEASE (!!) don't even think that what seems like a small verbal mis-step couldn't come back to whip you severely in court, and maybe even convict you.
Don't kid yourself, it ain't always the truth that wins trials. It is what looks most convincingly like the truth to a motley bunch of jurors in a courtroom six months or a year later, listening to a lot of people -- and not just witnesses -- many of whom were not there, and some of whom may have significant bias in matters like this (but it can't be proved).
Ayoob wrote an article about this a while back. Couldn't find it, but his advice sounded good at the time. Similar to Stephpd. Something like this: Tell the police respectfully that you are extremely upset, that you know how important this is, and that you will have a full statement for them after you have talked to your lawyer.
IF you feel clear headed, MAYBE say it was self-defense/defense-of-others, then STOP talking about it. If you fell clear headed, then MAYBE point out evidence (shell casings, weapon, marks/stains, witness, etc.) -- But don't try to say what it means, just point it out. (Reason for the latter: Cops are almost all good and honorable folks, but they need to see if a crime has been committed, so they are probably "tuned" to look for evidence of crime, more than evidence of your innocence. Possibly significant mind-set difference, not just word play.)
By the way, if you talked about the event at all after you initially said you want your lawyer, then say it again. Then stop talking again.
Just my HO, not advice. -- Doug
(PS/ Notebook. Could be good or bad. I'd say at least make sure your head is clear before writing anything.)