A few of the hints that point to rheumatoid arthritis over the other answers:

• Younger age of onset and female - rheumatoid arthritis is an autoimmune disease and can thus present in younger females whereas osteoarthritis is from wear and tear so it is usually older individuals (FA2020 p466 for osteoarthritis vs rheumatoid)
• Sparing of the distal interphylangeal joints (DIP are spared in rheumatoid arthritis) and bilateral - in the other disorders there is not necessarily selectivity for the PIP and MCP, and they would not necessarily be bilateral (i.e. gout is not necessarily bilateral) wheras rheumatoid arthritis is bilateral
• Pannus formation - the formation of nodular pannuses is characteristic of rheumatoid arthritis over other disorders (especially once gout is eliminated the presence of nodules points most to rheumatoid arthritis)
• SLE would be likely be associated with other associated symptoms (p470)
• Also the arthritis in lupus is nonselective for joint type
• Scleroderma does not commonly present with arthritis or joint pain (p473)