When should I get my surgery, by the latest?

I had an accident involving a chisel in woodwork three days ago, and I got it stitched up. However, the tendon that helps the front part of my finger is torn, and I cannot bend the first part of my finger (It happened on my left index finger, middle part). My doctor is trying to give me an appointment ASAP to a plastic surgeon, or hand surgeon, but my parents are a little worried. They told me that if I didn't get this surgery done ASAP, my tendon might lose flexibility and make it even harder to reattach it back, let alone even be able to stretch it. Is there a maximum amount of time that I MUST have this surgery before irreversible damage happens to my tendon? Thanks!