Daween, I would rather children are neither hit OR screamed at for "being too slow", Christ's sake. It doesn't have to be one or the other. Hopefully though what you saw was a snapshot of a parent having a really bad day and not what their lives are like all the time, anyway.
OP everyone makes mistakes, and I agree it sounds like an instinctive reaction. It sounds to me like you dealt with it well in the moment and I agree that it needs to be drawn a line under now, don't go overboard trying to "make it up to him". You did, you apologised, it's OK.
When there are potential development issues, it can help to use a different way of parenting. The typical reward/punishment models do not work when a child is behaving badly not out of choice but because they are lacking some kind of skill relating to their behaviour - for lashing out, it is likely to be the skill of impulse control and/or a tendency to find certain things more unbearable than most people would.
However the other two models often offered as an alternative often fall short as well: Positive parenting (where you reward/praise/encourage the good and ignore the bad) is not enough when you need to protect e.g. a younger sibling, a pet etc. Gentle parenting (where you see behaviour as communication, and generally avoid coercion/hierachical methods in favour of co-operative methods) can often be overly focused on avoiding conflict and lacks good guidance on how to impart boundaries in a situation where the child and/or parent struggles with this. But for me, the huge issue with both methods is that there is a gaping hole where there should be guidance for parents on what to do when you find your own frustration or anger raring up - there is much criticism in the methods for the kinds of things parents resort to when at the end of their tether - shouting and screaming, smacking or other physical roughness, threatening, criticising. And I'm not saying those things aren't bad, because they are. But it means when you're trying very hard to be the perfect positive/gentle parent, those moments when you lose it become this massive taboo that you can't admit to other people, and the result? You never get the chance to learn any skills to manage them.
Reward/punishment works very well when a child is making a simple choice that benefits them, because the reward/punishment serves to re-balance the current situation so that the action they want to do which is destructive (or annoying or mean or whatever) is no longer rewarding for them and they will then make a different choice. When a child continues to behave badly even when there is a clear system of reward and punishment in place, it can mean that either the balance is not right - OR - that the child is not making a choice in that way, that they are unable to act in the way you are expecting them to. When this is the case, it would be like punishing a child who needs glasses because they seem to be refusing to learn how to read. You aren't going to make them able to read by punishing them. The only thing that will help is to correct that deficiency in their vision. It's the same for developmental skills, although unlike vision these can generally be acquired through age and/or teaching.
The sort of "third alternative" then, is a model which is based on clear boundaries but recognises that children's difficult behaviours are not always a conscious choice on their end, supports parents, recognising that these are really challenging things to deal with, and helps children by supporting development of the skills they are lacking until they are able to manage them for themselves. Sounds like some kind of holy grail. I haven't managed to find any one "method" or buzzword for it but for me the methods/authors which fit to this kind of thinking and more importantly seem to work are:
RIE as a parenting method - I follow Janet Lansbury's podcasts on this topic which are free and easily accessible. She also has a book, but I didn't love the book. The podcasts and her articles are better.
The Whole Brain Child/No Drama Discipline - have not actually read this yet, but based on what I've read/seen in terms of reviews, snippets and interviews with the authors, it sounds like a fantastic distilment of everything. In fact I've bolded it because if you have a newborn, you probably don't have time to read lots of things - start here. You can get it on kindle and read during feeds if you have the energy. This is next on my list to read, but I need to decide which one and I try not to keep spending money on books before I have time to read them, so it's waiting for that as well!
The Explosive Child/Dr. Ross Greene - he has a newer book out as well, which sounds even better/more up to date but I don't know anyone who has read it. Also on my list to read.
ABC technique - this stands for Antecedent, Behaviour, Consequence. It's about looking at what triggers your child's behaviour and how you can help them manage it. Consequence does not always involve punishment, although it might. When it does, it's about creating that balance I mentioned earlier, which means that you have to be aware of the child's skill defecits which may be causing them to act a certain way and take these into account, because it is not fair to set a child up to repeatedly fail and suffer a punishment that they are unable to avoid. That is what makes it different from a standard behaviour > consequence approach. It's the A which is important.
BTW, if you do or like the principles behind positive parenting or gentle parenting, these kinds of techniques are very compatible, so I'm not saying that positive parenting or gentle parenting is wrong - there are many many excellent points made by proponents of both discipline styles. I just feel due to personal experience, the above offer a more rounded approach, which works better for children who may not be neurotypical. :) (And also those who probably are neurotypical... but particularly the kinds of children who struggle when faced with "typical" parenting techniques will benefit, I think.)