2002 has a bad tranny. Will the 2003 work in the 2002?

These both have 4F50N transmissions but you will want to have them side by side for comparing shift linkage and harness configuration to verify they are a compatible swap.

Odds are good that it will work. Ensure the TRS and shift linkage, harness, and harness connectors are identical. I would drop and clean the pan and magnet, install a Dorman 65241 drain plug (torqued 20 lb.-ft.), replace the filter, and reinstall the lifetime pan gasket, prior to installation. After installation, refill with Mobil 1 Synthetic Multi-Vehicle ATF. Change fluid and filter every 30,000 miles. ATXs are the weak link in all FWD vehicles and require extra care.

Thank You the shift linkage looks the same and the electrical plug in the top of tranny looks the same. I am not sure what the TRS is. I will take a better look at these items before starting to swap. Someone told me that the computer may have to be reset after the swap is done is this true?

Transmission Range Sensor (TRS).

The electrical plug on top of the tranny is for the TRS: sometimes called the Neutral Safety Switch.
If this isn't adjusted or installed properly or isn't working correctly, it can cause a no-start condition.
If anything needs reset, you may need an apppropriate scan tool to set up or verify final drive ratios to prevent speedometer errors but even that is unlikely...
Good luck and let us know how it turns out.