OK I sacked EDE and have NO human companions before i talked to the King
and hence I have the quest

The King agrees to allow me to take Rex for help.

BUT rex does not/ will not follow me.

I talk to him and obtain the choices:

1) How are you feeling boy;
2) I am still working on getting you fixed;
3) I want to take a closer look at you;
4) Goodbye.

After chucking 5 levels to finish Boone's quest I decided to do ALL companion quests before the DLC
but I am rapidly becoming bald from tearing my hair out

Any suggestions?
My char (like me) is female but surely that does not matter.

Take a closer look. I think you have to do that before he will follow you.

Tried that.
Dr said"cannot fix it if I cannot see it"
Went back to Rex...same dialogue choices...no follow