I've attached some photos of my infected monstera.

Thanks for the question.

I enlarged the pictures that you sent and can confirm that this plant has a common name of Swiss Cheese plant. More specifically it has the botanical name of Monstera deliciosa. Congratulations on your identification.

Before directly addressing your question, here is some background information on the plant:

https://abeautifulmess.com/how-to-care-for-monstera-plants/

https://www.thespruce.com/how-to-grow-monstera-deliciosa-5072671

https://plants.ces.ncsu.edu/plants/monstera-deliciosa/

With respect to the red rust patches on the leaves, this caused by some type of fungus. Without a detailed microscopic examination of the leaves, it is impossible to identify the specific type of fungus. However, most fungi infecting Monstera leaves and causing leaf spotting belong to a group known as Pucciniales fungi. I see that today you updated your question to be consistent with this. Most likely your plant came already infected from the nursery.

Your primary purpose at this point should be preventing this rust from spreading. It would be premature at this time to just toss the whole plant. There is little you can do for the leaves already showing symptoms. For this reason and as soon as you can, all leaves showing this spotting should be removed and discarded in a tightly sealed plastic bag into the trash. This particular fungus favors moist conditions. For this reason, avoid misting the plant. Rather, water directly onto the soil surface. Since this fungus tends to be rather host-specific, infection of your other plants would not be expected but certainly cannot be ruled out. For this reason, reposition your plant in a location distant from all other plants. Fungal spores are probably present on other leaves of your plant and on the surface of the soil. To combat this, go to a local garden supply store and obtain a fungicidal spray containing a copper-based active ingredient. Apply this spray to the other leaves on your plant, always following the directions on the spray container.

Ideally, it would be best if you would repot your plant into a sterilized pot. To do this, rinse a pot with a bleach solution (1 part commercial bleach to 9 parts of water). Then thoroughly rinse the pot and let dry. Use fresh potting soil. If complete repotting is not feasible, try to remove as much soil as possible from the current soil surface and replace with new soil. Be careful not to damage any roots in the process.

If you continue observing significant numbers of leaves being infected, then you should toss the plant and replace it with a new one. If you go this route, make your purchase from a different nursery.

See the following for further information on these and related points:

https://monsteraplantresource.com/rust-fungus-on-monstera-6-causes-and-how-to-fix-it/ - :~:text=One of the most common,and disinfect them between uses.

https://xanhxanhurbanforest.com/rust-spots-on-monstera-causes-treatment/

https://www.evergreenseeds.com/rust-fungus-on-monstera/

Good luck. Please feel free to get back to us with any further questions.

Glad to have been of assistance.  Good luck.  Thanks again for using our forum.