Could it be that he is anxious about seeing a psychologist because he
a) has no idea what it would be like and/or
B) because he has an idea that seeing mental health professionals would label him as a "mad" person, even if only in his own mind.
My ds had very immature ideas of what people with MH problems are like until his own sister needed a CAHMS referral. Dd had a far better idea because she had once been treated for a physical problem in a rehabilitation clinic where a substantial number of the other children were in for various MH issues. She had seen that they weren't different or scary people, just other children like her who were ill in a different way. It made her realise how many of the perfectly ordinary, popular children she might meet in schools across the city might have needed mental health support at one time or another. They don't stick a label to your forehead forever after.
It may be that his ideas of what a psychologist/psychiatrist appointment is like are coloured by oldfashioned films. Would it help to reassure him that he will not be required to lie on a couch and reveal his innermost thoughts to a person in a white coat? From my experience, this is what a CAHMS appointment would probably look like:
there would be a brief introductory meeting where the professionals introduce themselves
you would then be asked to leave the room
he would probably be asked to fill in a questionnaire about how he feels in various situations, to establish that anxiety really is a problem (you will only be shown this questionnaire as and when he agrees)
hopefully he would then be given some CBT-based training- it would be explained to him that the aim is to give him the techniques to handle his own anxiety and take control over his life so that he doesn't have to be dominated by hurtful feelings
there would be techniques both for general relaxation (say, to ensure a good night's sleep) and for specific situations which he has pinpointed as problematic
everything would be done in discussion with him
he would be asked to practise the techniques he is taught and keep a record of how it works
they would discuss plans for returning to school and managing his anxiety
if he wanted them to, they would liaise with school to make sure everybody is onboard with the new plans
everything they told the school would be confidential: it would only be known by designated people and not gossiped about in the school corridors
given his age, they would probably only suggest medication once they have tried other paths and really weren't getting anywhere