It is really hard when they're so badly affected by teething. When they're clingy it's an expression of their need for comfort and security and the only way to get through it is to give them that. Trying to force them to be alone when they're not comfortable with it will only make their clinginess worse. It is a phase that will pass when he's feeilng more comfortable, I hope you can find a way through for now.
All the best