You might consider an ultrasound scan: good for superficial soft tissue injuries with the added bonus of being able to visualise moving strutures. Nothing like as expensive as an MRI if you go privately.
Recent advise from a physio (for a knee, but the principals the same) went along the lines of - "MRI? what for. Unless you need surgery, the treatment/rehab will be exactly the same anyway. MRI is only usually a precursor to surgery to allow the surgeon to see exactly what they'll be dealing with"Given that its highly unlikely you're going to need surgery on it, then why bother? Just crack on with the normal A2 pully rehab regimes, and given time, you'll be back climbing again. (caveat: I asked my physio about it since, I expect just like you, I really wanted to know *exactly* what I'd done and to what extent, but her answer seemed to make sense. I'm quite a way down the line with the knee know and the physio is working and I'm back climbing and gaining confidence it the knee again.)
As others have mentioned, ultrasound would be a good place to start. James @ Sheffield Climbing Clinic uses one if you're Sheffield based...[Relevant aside - I saw Volker Schoffl in Germany recently about a chronic PIP joint issue, and ultrasound was his instant go-to tool]
