1998 Cadillac CTS wont shift

Any codes? If not try going to an oil change place that can "flush" the tranny without dropping the pan.
Are there any codes? MIL on? If so try a tranny shop that can read the tranny codes for Caddy.
There is a problem called a TSB if there are codes and no shift between 2nd on some trany's and 3rd on others, The power supply curcuit to theTranny solinoid could be an issue! How long have you had the problem. If it's related to this TSB your instrument cluster will be going out!
Reference numbers=01-07-30-002E Date of issue: 9/23/2005. Covers all GM 2006

and prior passenger cars with 4L60-E, 4l65-E, 4L80-E, and 4L85-E transmissions. The solution is a new wiring haness and connector.

Caddy didnt make a CTS that year, catera?

Do you have lights in the shifter?

There is a plug on the tranny that gets corroded, pop it off and check, it comes from the computer to the shift solinoids, other wise the shift solinoids need checked, dont waste your money on an tranny flush, fix the prob first

Gee I thought I said that already.