Can you chat with him about the feeling sick being a symptom of anxiety, and teach him strategies to try to calm that - deep breathing, eating a ginger snap, whatever (doesn't matter if it doesn't have any evidence, if he thinks more calmly as a result, it could help!) - and at the same time cognitive behavioural therapy strategies regarding thinking changes. That way he knows he is being listened to about feeling sick, but also that it is something he has to learn to deal with, rather than something that will get him out of things. And if the strategies can lessen the feeling of wanting to be sick, then that might ease the worry about it happening, if that has then become an extra worry on top of the others.
If he is most anxious about detentions, then it might help once he sees other people starting to get them and realises that getting into trouble in class isn't the end of the world - attention isn't on that person forever, the teacher forgets soon enough and treats them normally again, etc. (I'm trying to remember the sorts of things that made me anxious at school, and that was one of them - the attention that would be on me if I got told off!). Also for me, the fear of the unknown with detentions was worse than the thought of the detention itself. It was fear of not knowing where to go, what to say, what to do, what would happen. If you can find out if he is worrying about anything like this, you could perhaps get the form teacher or whoever to talk him through what would happen in the worst case scenario and he did get a detention for forgetting something.
Strategies like going through his bag, having a list of what should be in there, writing down important messages etc, are all good. Having a spare pencil case in his bag, and one at home, so that the school one doesn't ever have to leave his bag can help. Spare pens to loan out to others can help. I certainly found it comforting to have spare things that I was unlikely to ever need, but I felt more reassured with them - so things like spare ties or PE kit on days that I was unlikely to need it, or extra locker keys/codes etc. Not so much of this that he becomes a bit obsessed with never breaking a rule, but just enough to have that feeling of reassurance.
Lots of talking through 'what ifs', even if he won't/can't verbalise the things he's worrying about to you - and they might be incredibly minor details. I worried hugely about having to go and see a teacher outside of class, to find out about clubs or to pick up something like missed notes or whatever, or even to go to another classroom or reception to get a message or ask for something - I didn't know whether you knocked or walked into the big office, how you got the attention of the receptionist when there were lots of people working in that room, what you said, etc. I spent ages worrying about having to go for a message (and I was good and quiet, so the sort that would be chosen by the teacher to go ask for something etc). And yet it wasn't the things that you'd expect someone to worry about - not remembering the message or finding the room or anything, but the whole 'do I knock and what do I say' thing. It can seem incredibly trivial, but panicking for an anxiety struck child. I used to panic over ringing the bell to get off the bus, too, and was always relieved when someone else did it! Someone talking me through a lot of these things, step by step, and reassuring me that attention wouldn't always be on me if I did them wrong, might have helped. A lot of it was just time to get used to it, to watch everyone else from the sidelines a bit, not be forced into things but gradually allowed to find my own way etc.
Also to be reassured that it was OK to be sad/unhappy/anxious. And that sometimes you didn't have friends, or ate alone at lunchtime - I did it for several years! - and that it didn't mean anything was wrong with you. It's lonely, yes, but that wasn't what made me most anxious, actually, it was the thought that I shouldn't be like this, that something was wrong with me, that my parents would be disappointed in me etc. So reassure him that he can cope with being sad/anxious, it isn't something that has to be solved immediately, that you aren't disappointed or cross with him.
There's a book called 'what to do when you worry too much' that is well-recommended, although he might be too old for it now. But it might have some strategies that could still be useful.
good luck. As a very anxious child, I know how important it is to have supportive family!