Have your engine checked because there is something going on.
Let’s look at just how your throttle works with a little history to start. About 30 years ago, a switch started in the auto industry. Slowly, as digital electronics became more and more robust, “drive-by-wire” began to replace mechanical linkages. Before “drive-by-wire,” a throttle system was fairly straightforward. The accelerator was linked to either the carburetion or fuel-injection system by a series of linkages. You pressed on the accelerator and the linkages opened up performance as more air entered the fuel system and as the transmission kick-down activated.
This changed with full “drive-by-wire.” Instead of relying on mechanical linkages, the system uses a series of sensors such as the throttle position sensor and control modules (essentially microcomputers) to maintain, increase or reduce your speed. The system monitors a series of voltages that whose basics are stored in non-volatile memory. In its monitoring, it watches for major differences between sensors and modules. If the range is too far out of whack, the car is placed into either a safety mode where the engine shuts down or limp-home where the engine and transmission go into second or third gear and remain there so that your car can move until you can get it to a service area.
If things get too far out of whack, the throttle control motor cuts in and physically moves things about until the engine shuts down.
So, you asked what I would recommend to be checked. The answer is relatively simple. Take an OBD-II reader, plug it in and look at throttle-specifid error codes, if they have accumulated. If they have accumulated, narrow down the problem and have it fixed. If, on the other hand, there are no codes for the specific problem, see if there are any codes relating to the fuel system as it may be that an outboard system is impacting the throttle.
In any event, the throttle system needs work.