Hi,
I suggest you split your streams into two, at points from where you consider upstream and downstream well as appropriate for your study. Do the following when splitting: make sure you have same StreamID for both parts (line) of the split stream. Then, depending upon your upstream part or downstream part, add a text field, DirectionofStream that will say "upstream" or "downstream".
Next use the near tool, to get a count of points (wells) for each stream. The result will depend on your definition of nearness.
Later you can join summarize all your streams (lines) using StreamID and direction field.
regards,