I agree with your assessment Chris and that sounds like a good rehab which I will most likely follow. I'm still going to go to the doctor just to get everything checked out and to be safe, he is a family friend of ours and will give me a very honest assessment.
You have a partial tear if your description is at least reasonably accurate. No need to see your doc in my personal opinion. Wait 1-2 days and get right back on the bench. Start VERY light (just the bar). Do 1-2 sets of 20 reps through a complete ROM. Contol the load and do not move quickly. Bench every day like this increasing the load daily in small increments (5-10 lbs max) until you are no longer able to increment and match reps. Once you reach that point take an extra day between sessions and resuming increasing the load with each session. Once you reach a load that is getting close to your previous best with 20 reps start spacing out your sessions normally and begin dropping the reps and increasing the loads.
The above is exactly what I did to rehab a worse tear than you are describing.
This is my personal advice, you should do what you are comfortable doing including seeing a doc if you want to.