So, I'm curious, the particles in that shot look good. Is there a reason to not use the ones from that shot above? Looks like they are free.
If you want to create them, there are ways however. AE has it's own a particle generator and then there are things like Trapcode Particular.
I'd search for tutorials on how to make dust or rain or something and modify that to sideways, play with wind and gravity if necessary but that would really be the approach.
Andrew Kramer also has some free dust particles that are made from flour I believe that has random movement but less wind.
Did you ever solve this particle issue to your satisfaction? What did you end up doing? Please let us know for the benefit of the community.