I agree with the others saying don't remove the story/contact with you.
I think it's OK to be honest with him about still feeling sad/angry about what happened if you're struggling to lean into normal affectionate or silly bedtime games, but definitely reiterate that you love him and try to keep his routine as normal as possible.
When you are feeling calmer in the coming days it might be worth seeing whether he will brainstorm with you some kind of plan for what to do if he ever feels so (angry? Trapped? Excited?) that he wants to bite, as a potential preventative measure. You might also find the book The Explosive Child helpful if you haven't read it yet. It has some very good advice for helping navigate the "why" of incidents like this and how to do preventative work between incidents to try to reduce them overall.
Sometimes when they tell you a garbled version of events which doesn't make sense and includes a lie, it can be complete nonsense because they know they are in trouble and they are fishing around for an excuse/justification but they aren't yet very good at understanding what makes something believable or excusable. That's one thing (and might be a piece of information on its own if the things he chooses are out of step with how a 6yo would usually lie). But OTOH, sometimes the confusing explanation can be almost metaphorical or a sort of skewed interpretation of what actually happened, and sometimes it's possible if it's not too distressing to dwell on it to tease this out into an explanation which makes more sense.
For example DS2 (8, ND) for at least the last couple of years will sometimes come out with extremely garbled versions of events which don't make any physical/logical sense - now we might assume that it's just a straightforward lie, but he will be absolutely vehemently insistent that this IS what happened, and in contrast to when he does genuinely try to lie, his whole demeanour is different. When he is actually lying to deceive, he can't look you in the eye and if he does he can't stop a giant grin from appearing on his face, to the point that sometimes he hides his mouth in his hands while talking. His voice also goes high pitched and playful, he can't keep it serious or nonchalant. His 4yo brother can lie convincingly and picks believable things to lie about, aside from not always correctly gauging what adults can infer without being directly told.
OTOH when he's explaining after an incident which seems inexplicable from the outside and the explanation makes no sense, what I've come to realise is usually going on is that when he is in a high emotional state, whether that's excitement or fear or worry or anger or upset, it's like some of the bits of his processing brain sort of get blocked, or the message doesn't get through properly or doesn't get encoded into memory properly, and so the version of events he remembers is literally different from what happened. I can't obviously see into his brain to understand whether his recall is the bit which is garbled or whether he is recalling accurately and he experienced the whole thing differently to others, I suspect a bit of both, because he will say things like "I definitely left my book at school" but also "I was at X's house and she rubbed everything out" (and he did not return to school after being at X's house, so the book could not possibly be there and he could not have remembered leaving it there - he probably transferred this memory from a different school day) and at other times, if he is in a highly emotional state, he will interpret things in a different way to what is actually happening, e.g. I remember being very disturbed by an incident when he was 5 and he was angry, I was standing more than arms' reach away from him, and he was pulling his own (long) hair and screaming "Why are you hurting me Mummy??? Why are you pulling my hair??" I can't obviously be sure what exactly was going through his head at the time, it was one of the things that led to him getting assessed, but my general impression from some other stuff that was happening around that time was that when he was getting into an overwhelmed state he was casting around for the nearest safe person to blame, which was generally me, and then every possible thing which was overwhelming him got conflated in his mind with Mummy having been the instigator of all of it, which allowed him to have an outlet to rage against. He still does this although to a lesser extent and no more self harm thankfully - but he'll come out of school and scream at me that I've made his teacher hate him - that's when I know it's been a complete shitter of a day for him.
Anyway, I hope the GP visit is useful. It's tough dealing with these kinds of things so be kind to yourself and do whatever you need to do after he goes to bed.