You can throw your shirts and hoodies in the wash, they enjoy the bath and love the water. Just make sure that:
> They are turned inside out (print on the inside)
> They are washed with similar colors
> They are not washed at more than 30°C/90°F Don't bleach
> Try avoid drying them with a machine, heat and cotton are not nice friends. You can get away with putting them in the drier with 'Delicate' settings if you absolutely need to use the dryer.
> Do not iron on the print. Turn the shirt inside out and iron on the backside.