Based on what are you making this determination? I have known people with fybromyalgia and chronic fatigue and it's outright cruel that a lot of people (including doctors) are telling them that it's only in their head.
Psychosomatic doesn't mean "only in their head". It's the opposite really, it accepting that the symptoms are real, but are being triggered or aggravated by something mental (stress, for example).
Based on our knowledge of how vaccines work there is no reason to think they would actually help after the active viral infection has cleared. But psychosomatic symptoms are extremely common.