I also own a 92 caddy deville and had the same sort of problem.
My problem continued to worsen until it would stall constantly.
My mechanic replaced the ignition module and the problem ceased.
The module cost was approx 140 dollars canadian and around 2 hours labour to trace the problem.
I have a 1993 De ville and had the same problem. However, I discovered that all it needed was a 30 amp fuse. Check the fuses that are located in the compartment directly underneath the glove box. This compartment has to be unscrewed to gain access. Hope this helps.
Mind also hesitated, but the use of a fuel system cleaner in the gas tank virtually cured the problem. I have had to do it twice, for a total cost of 6 bucks... probably cheaper than replacing the injectors.
Investing in a shop manual and learning to use the on board diagnostics will save you the price of the book, the first time you use it.
First start the engine and press the off + the red warm buttons on the A/C controls. Both at the same time and hold them until the dio system shows on the a/c panel. Then watch the fuel system panel and write down the codes that show. Then push the off + high fan buttons and hold until F00 shows on fuel panel, then Off+low fan until EOO shows on fuel panel. This deletes all set codes stored in the system. Then press auto button to exit dio system. Drive the car a couple miles and then re-enter dio as above and let it scan for any codes that set again. This system can be a great help, when you learn to use it. Not sure, but you may be able to Google the codes to see what they are.
If you plan on keeping the car, the shop manual is well worth having. It has the codes and what they mean in it.
Look in the back of your owners manual for an order blank.
Helms sell the manuals.