If there REALLY is a break in the pipe,
All your sucking and blowing
will make it a little worse.
Slow down and think about what direction the drain is going out of the house from the shower.
Does it go out the side of the house and do a 90 degree turn to the street, or the alley?
Sometimes a foundation will shift over . . . 40 years or so and the drain can break right at the side of the house where it turns 90 degrees.
That happened to my 80 year old clay pipes here in Denver.
Anyway, it is good to find out exactly where your drain is and how it gets the water out of your hands. Could be a root, a crack, or a bunch of hippie hair.
Spend $50-75 and call a rooter guy, and if that doesn't do it, have them do the camera bit for a little more. Some guys have a fish-tape with a transponder on it, so you can go outside and see where it is from above ground with a metal-detector type thing.
Fun stuff! NOT. good luck to you!