When you're going to do some external jobs, (it doesn't matter that the job is own trailer, or not) you've to use the latest version of the game. World of Trucks isn't compatible backwards, so you're right. If you've played on your profile with 1.38 in singleplayer, and then you downgrade to 1.37, and use the same profile (with which you played 1.38) that may be a possible problem (because saves also aren't compatible backwards through the game versions).
If the problem isn't with the profiles reverse compatiblity, try to remove/unlink World of Trucks in the game files (because maybe it is linked, even if the game doesn't show this).
- World of Trucks connection data (e-mail and password) is stored in: Documents/Euro Truck Simulator 2/profiles/<your profile/profiles>/profile.sii -> in the profile.sii, scroll down to the bottom until you find to lines: online_user_name and online_password (you need an SII_Decrypt to make the file "readable"). If there is anything between the quotes, clear it, and just leave the two quotes both lines, without a space between them.
If your problem isn't solved, send a crash log, and we could help more, or try to verify integrity of game files on Steam -> ETS2 -> properties -> local files (to be honest I don't think that this will solve the problem, but without a crash log, give it a try).
kinit, the elegant sponge