Shut up. Don't write to your ex. Have no involvement with your ex that you don't have to have. Women's aid told us to say "your child is fine, they're doing well at school and your next contact is at X time on Y date" and nothing else to exes, just that, on repeat, for every time they contact you regardless of what they say. Basically, don't give them a reaction or any ammunition to use against you.
To your son, just stick to the truth:
You didn't tell his father that he has X condition.
You don't think he has X condition.
Your son has been asking questions about it and mentioned it to you a few times, that's why you told the psychiatrist that you thought him, your son, was concerned about it.
You aren't concerned about X condition because you don't think he has it and you never did.
That way you're not saying his dad is lying. You don't know whether his dad is lying, which is likely he is, but you don't know for sure because you said yourself DS makes things up sometimes. So stay away from that accusation.
Basically don't concern yourself with what others think and just state what you think. Stop trying to work out what's going on. It doesn't matter what's going on. YOU aren't doing anything and if someone else is, that's out of your control, so don't think about it. Step back from it all. "Not my circus, not my monkeys". Just deal with your life, nobody else's. Your son thinks that you think he has X MH condition, you don't think that so you correct him, that's all. No need to make more of it.
The less you have to do with your ex the better. Then next time you get told "dad told me that you think XYZ". You can answer "how would your dad know what I think? I haven't spoken to him in 3yrs. Ignore anything he says about me, he knows nothing about me. I'm here if you ever need to ask anything". As he grows up he'll hopefully realise his dad lies.
Is my son going round saying ' my mum said I have X condition ' - is this a problem for me? Is he saying that in school. This is my worry.
No it isn't. What others think of you is none of your business. You can't control others thoughts or actions, including your son's. You're so caught up in others dramatics and you don't have to be, just step back.