How would a person in the middle ages carry clothes or other small items with them across long distances?
if they're poor and on foot, they'd tie them up in a piece of clothing or a cloth of some kind and carry the bundle or sling it on their back... if they have a horse, they'd tie the bundle onto the saddle, or load it all on the horse and walk, leading the animal... if they have a cart [hand-pulled/pushed, or animal-drawn], they'd load their items in that... if they're wealthy, they'd have a cart of some kind to carry chests packed with their belongings and either ride in a carriage, or on horseback...
Depending on their social class, and the journey, they had various kinds of satchels and sacks, as well as a, again depending on era, location and class, ways of storing small items in pockets and sleeves. If you want pictures, Google Books of Hours Calendars or Books of Hours Labors