The advantage of having your own OBD reader might be that often the system only saves the 'codes' for a limited time. If so, by the time you take it to a shop it may have been operating normally long enough that it will have erased the code.
That depends on the reader. Cheap ones will only show active codes. If an active code exists long enough it becomes a "permanent" code that can be seen, even if the original issue has been resolved and the active code no longer exists.
But if you are not already proficient with OBDII and tracing codes, getting a reader for this issue probably isn't going to help. The professional tech will already have a capable "reader" that he can see the codes with, as well as live data, built-in tests, and two way communication which allows him to change parameters "on the fly" and instantly see the results.
A cheap reader doesn't have that.
An abnormally shifting transmission needs an expert diagnosis.
This is not a leaky gas cap or failed purge valve fix.