This is what I did.
Had a vertical condensate discharge, which dumps the water to a tiny pump.
Added a P-trap to the vertical line as shown in the picture.
The way you installed the P-trap will work but it really should have gone in the other way around. Then, you would only need one elbow and a coupler instead of three elbows.
The way you have it the water backs up all the way to the height of the line on the discharge side of the P-trap. If you install it the other way around then you only have water in the P.
Look at the P-trap under one of your sinks to see what I mean.
EDIT: However, since this a forced air system you need to check how many inches of water differential pressure you have. Once you know that, you will know how big your loop seal needs to be. It could be that the P-trap might not have a big enough seal on its own.