He isn't 'faking' it necessarily as in actually making up symptoms- he is probably having symptoms, possibly of depression and anxiety, such as chest pains, tightness, breathlessness, irritable bowel, dizziness and so on. Those produce real effects in the body and then the mind does the rest.
I have a family member who has been like this since young. Unfortunately, no amount of sympathy/psychiatric intervention makes a deal of difference and they pop off to A and E or the doctor all the time even though when they get there, there is little if anything wrong with them. It's a psychological illness.
As to whether I would carry on- no, I wouldn't. My relative is still going on about his imaginary illnesses for 50 years and it isn't stopping (of course, one day he will be right, he will have something horrid!) It's draining and awful for their partner and nothing actually stems the malfunctioning thinking (tried anti-depressants and so on but always has 'massive side effects' and comes off them within a day).
Yes, it is linked to trauma in early childhood, and yes it is very sad, but if I had a choice, I would not live with this whatsoever as it's a very negative and draining way to live, especially with someone for whom this has become part of who they are, and not just a temporary dip in mood. Get out OP, honestly.