Hi Yael

This question is difficult to answer. We all heal at different rates. This depends on age, lifestyle, ethnicity, and a few medical conditions. Fortunately you have a very good blood supply in your vagina, which will help you to heal. However it can take several weeks for a wound to heal. Even though there may have been a lot of blood from this injury, the tear may be quite small and not cause you too much problem during birth. The location of the tear is also something to consider.
You do not say when your baby is due but from your post I guess it is within the next 3 weeks or so. If this is the case I would expect you to tear. This does not mean that you will, nor does it mean that if you tear it is going to be very bad. In fact if you do tear during birth the tear may be no larger then the tear you have now.

I hope this answers your question and perhaps helps you not to worry too much.