I believe the total length of 1.5 inch vent can be 25 feet total. I could not determine from your picture how you attached/supported the pipe.It's good practice to include pipe supports close to tees. It wouldn't hurt to put in a support at your short horizontal vent pipe, but I tend to overbuild. Make sure that the horizontal pipe is sloped 1/4 inch per foot.

See Section 905 of 2012 International Plumbing Code for venting connections. With your T into shower vent: vent connections must be at least 6 inches above the fixture/flood level being vented.