All transmission codes are "P" codes, so your scan tool should be able to read them........
Certain transmission codes will not turn on the CE light right away, they are "pending" codes(have to fail twice in a row in a "drive cycle" to turn the light on).....
And sometimes, other codes will force the PCM to react differently, for example some codes will force the coolant fan to run....
Usually, when you are "feeling" hard shifts, that is because the PCM is commanding "full line pressure", which is usually a result of a code failure, even if the CE light is not on, there could be one in history....
Have you checked transmission fluid level and condition?