Problem with engine at speeds above 50mph

I have a 2000 Corolla with about 147,000 miles. At idle it runs very rough, but can accelerate up to about 50 mph. Then it starts to cough and wheeze and run roughly again and won’t accelerate any further. It feels like the engine will shake itself off its mounts, so I slow down and stay under 50 mph. I replaced spark plugs and a repair place hooked it up to a computer. They then told me it needed about 1800 dollars worth of repairs to replace the valve cam I think they said. I’m skeptical and wonder if it just needs a tune up, . It has not had one since I bought it at 128,000 miles, and II don’t know how long it had been prior to that.

Can you tell us exactly what they wrote on the shop order?

19,000 miles is not enough to cause the plugs to erode sufficiently to need another “tuneup”. You have something else going on here. There are numerous possibilities, including but not limited to a compression problem on one or more cylinders due to a prior oil depletion incident, a blown headgasket due to a prior overheating incident, a plugged cat converter, and oil-fouling of the spark plugs due to cylinder damage (again due to a prior oil depletion or overheating incident). We need more information to even begin to guess.

check the timing. quickly.

How much oil does this engine consume?
How long did it take the OP to accumulate those 19k miles?
If this engine consumes a lot of oil, it is entirely possible for the spark plugs to be have been oil fouled or clogged with carbon in just 19k miles.

And, if the engine does consume a lot of oil, then the next step–unfortunately–will likely be the replacement of the expensive catalytic converter.

This 14 year old car could be a sick puppy at this point, and diagnosis should include a compression check and a check for emissions in the coolant.

How well has this vehicle been maintained?

This does not sound like a simple fix.

And I’m not buying that it needs a new Cam shaft. That requires more diagnosis then just hooking it up to the computer. And they don’t just usually go…especially on a vehicle with only 127k miles…UNLESS IT WASN’T MAINTAINED PROPERLY.

Has anyone checked the valve timing? I think this vehicle has a chain…but wondering if the chain jumped a tooth?

If the valve lash has never been checked a burned valve is possible.
Did the shop do a compression test?