My experience is that physios don't tend to know very much about pulley injuries and how to treat as they don't get many patients with this injury. Maybe worth it if you can find a physio with some experience/a climbing physio?
Also, not sure on the details of your insurance, it may be worth saving the outpatient care allowance for a more worthy injury later in the year. You only need to think about that though if you're injury-prone like me!