I had my first shot two month ago also. I am scheduled to go back on Oct 17 also. I, too have been bleeding continually for 35 days and counting. Is this normal... too bleed continually.. not spoting... but continually like a regular period?
Should I go back to see my doctor?

When first introduced to the Depo shot, your body can take some time to adjust. Having irregularities in you period, even continued bleeding, is normal... while still I think 35 days is a bit much to put up with.

It can take your body up to 6 months to adjust to the shot, then for the majority of women, the shot stops your cycle altogether :)

It wouldn't hurt to give your doctor a call to ease your mind, most offices have a nurse line so you can speak to someone the same day and get some relief.

After my first shot (I didn't get another one) I had my period for almost 2 months...

I took the depo shot for almost 2 years and never had this problem. I def think you should give your gyno a call and fill her in. It doesn't sound normals to me. Maybe a few weeks, but 35 days seems to be 2 much.