Clicking Sound When I Accelerate?

Before I start I'll say that I drive a 1990 Buick LeSabre with cast iron heads (so they don't melt as fast as alluminum ones) The other day when I was driving, the "TEMP" light came on in my car (I hate that it doesn't have an actual guage). I immediately pull the car over and wait a couple of minutes. I start the car again with the "HEATER" setting cranked all the way up because I heard that's a good way to keep your car's temperature under control. The light never did come on again. However, down the road I start to hear clicking. Rapid clicking. The speed of the clicking increases even more if I accelerate...and the car begins to wreak of over-heating. I knew I had to keep going though because I was in the middle of nowhere and I had only a couple of miles to go to a gas station/rest area....just as I go to pull into the place, my car shuts off and I become very aware that something's wrong and I fear that the engine may have seized up. When I get out, my engine looks like 9/11. I waited about 45 minutes, put as much water in it as I could, and finished the remaining 4 miles to get home without any problems, but the clicking remains. Also the oil is just freaking filthy. What do you think happened? And would you say it's safe to drive the car now without fear of destroying the engine?

Clicking from an engine is often lifters.
Clacking is often wrist pins and rocker arms.
Knocking is often a crank.

You may have grooved a cam lobe.

Something zapped your cooling system.. thats a worry.

Seems like new oil and filter, check your water pump and belts for a start.
Hopefully its just a stuck lifter and it will fill.

If the oil is as you say (filthy) you may have coolant mixed in with it and you should be sure by having a pressure test done to make sure that there is no mixing,after that you can check why it overheated in the first place,good luck
Please post back with your findings.

I believe it could be the connector rod in one of the cylinders...it broke off but has yet to go through the engine block. It still runs as of now..if this is the case, can't I still run this car on its 5 cylinders(even though it's inefficient)?

I believe it could be the connector rod in one of the cylinders...it broke off but has yet to go through the engine block. It still runs as of now..if this is the case, can't I still run this car on its 5 cylinders(even though it's inefficient)?

Sure it may run, but if you have something broken off inside the engine, it will soon go through the block or head, and leave you stuck in traffic or in the middle or nowhere.