The engine rpms rev when shifting

Sounds like an electronic pressure switch or electronic governor. Your engine check light should be on or intermittent and it should have a code. A lot of parts stores or transmission repair shop should be able to tell you with a code reader.

1 Ck A/T fluid level & quality
2 Scan/ck for code(s)
3 With scan tool connected,road test vehicle/Ck parameters....
....time for a pro !!

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TPS SENSOR.
IT CONTROLS SHIFTING AT THE RIGHT TIME
AND COULD ALSO CAUSE ALL OF THE SYNMTHOMS
THAT YOU HAVE LISTED SOMETIMES WITH OUT GIVING YOU A CODE GOOD LUCK

run fault codes and look for a problem TCM. The problem is the engine at idle and gear changing is when the management system is trying to select the best gear for the rpms and as soon as it selects up the rpms drop so it shifts down and the cycle is repeated.

It winds up in 1st and then shifts right from 1st into 3rd. Then never shifts into 4th. Plus rev is gone. You broke the sun shell. The transmission will need to rebuilt or replaced.

You most likely have a broken sunshell inside the transmission. They tend to go out when the transmission is shifted to drive when while still rolling in reverse.

bad transmission

Did the 'Check Engine' Light come ON? Whenever the 'CHECK ENGINE' light comes on, the ECU (Engine Control Unit) sets a Diagnostic Trouble Code (DTC). These codes identify the particular engine management system which caused the light to come on.
You'll need to use/find an OBDII (On-Board Diagnostic) Scanner to retrieve any code which have been stored in the ECU computer. Afterward, we might be able to help you DIAGNOSE and perhaps eventually fix the problem.

Have he transmission drained and the screens cleaned