Rose rust, yes, but the poor thing will never be very healthy contained in a pot. Unless its a miniature or dwarf/patio rose, they really don't do that well in containers over time. If you can find a space for it in the ground, do so, and prune back to outward facing buds on each stem, taking any topgrowth which looks unhealthy before you plant it out. Burn (if possible) any unhealthy leaves/growth, particularly parts with rust, and remove fallen leaves from the ground and surrounding area. The rust infection shouldn't affect your plants apart from your other rose.
It would be useful to know which variety of rose it is to give proper advice on pruning, which can help with reducing the incidence of fungal infection by increasing air flow through the plant. It will help the plant's health if you add composted manure to the planting area when you plant it out, and to feed it in Spring and again in summer with a specialist rose food (don't know where you are, but something like Toprose in the UK), and have a spray such as Roseclear Ultra at the ready. Most roses need spraying fortnightly with a product such as Roseclear from late spring through to autumn to keep fungal infections and aphid infestation at bay.