Hypo/hyperthyroidism and mental disorders, can these cause relationship problems?

Sure. Relationships (especially new ones) can be fragile and delicate. Sometimes even small things can upset them - the thyroid hormones effect moods, attitudes and behavior as do mental disorders. Those are really involved in relating to others - so yes! you might buy a little understanding or time if you tell the person you're not always well - but you also need to get better. See a dr. For an eval!