I drive a 1995 Ford Thunderbird with a 3.8-liter V6 and a five speed manual transmission. The car now has about 98,000 miles.
When I'm driving normally and shifting into third or fourth gear I notice that the RPMs go up for awhile and then settle down after a few seconds. It seems fine in other gears.
I think your clutch is slipping. The flare up of RPMs immediately after a shift is caused by a worn-out clutch disc that can no longer lock the engine to the transmission securely. You will often notice it first in the higher gears.
On other vehicles I would suggest a clutch adjustment to see if it helps, but the Thunderbird uses a self-adjusting hydraulically controlled system.
The life span of a clutch varies greatly with the driver, but 100,000 miles is just about average. Have it checked out, and once the worn clutch is confirmed I would suggest using a factory replacement from Ford. Also be sure that the flywheel is resurfaced or replaced if necessary. Otherwise you'll have a brand new clutch that chatters during engagement.