Solely based on the codes you provided, it is not a transmission issue. P0136 looks like an O2 sensor circuit malfunction (Bank 1, Sensor 2) and P1151 seems to be the upstream bank 2 sensor indicating lean. A cursory glance online shows the best place to begin would be checking for vacuum leaks and exhaust leaks along with examining the wiring harness for the O2 sensors.
A possible troubleshooting option (which I have never tried nor do I know if it will work as I say) would be unplugging the upstream O2 sensors. In theory, this should force the vehicle into open loop fueling. If your problems disappear, your O2 sensors may be to blame or you may have an exhaust leak. Basically anything which could cause faulty readings from the O2 sensors is possible. If your problem is still there, then a vacuum leak seems more likely. Once again, I cannot guarantee unplugging the O2 sensors will cause open loop fueling. Possibly another member can confirm or deny. Additionally, tampering with the emissions system is illegal so this should not be used as a fix but a troubleshooting method.
I'm slightly confused regarding your description of the transmission shifts, etc...so I cannot say whether or not you have an issue with your transmission as well.
