Welcome to the forums and thanks for being here.
As a young person hopefully I can offer some input here - I can see both where you and your son is coming from. It sounds like a bit of a tricky balance in wanting to get him help and not wanting to force him at the same time.
I'm wondering though, what about seeing the school psychologist or the doctor 'ruins his life'? Is it the idea that he's forced to talk to people he doesn't know? That other students might find out? That he has to be labelled with a mental illness? The stigma of something going wrong? The awkwardness of being in therapy forced to talk about your feelings? These are just ideas that I'm floating with here but I think it would help to get to the core of why he doesn't want help.
A big part of doing that is having the conversation. Given that he's already opened up to you - it's a good sign that he trusts you. So being able to gently poke or nudge him into talking more can be a good next step.
Once you are able to understand the reasons why I feel like it will be easier to tackle them so he's not so reluctant to open up.
The other thing that comes to mind is giving him options. The first thing that everybody thinks of is straight up therapy; but sometimes just reaching out can be broken up into tiny steps. Perhaps that might be looking at things online, talking to young people (like on here) or just seeing what things might be like.
There's a few websites here targeted at young people which I'll link below -
Both headspace and kidshelpline also have web-chats which is a great way to be able to open up at a pace that's a little less intimidating then a GP or a school psychologist.
Hope this gives you a place to start,