WARNING: CTD BUG EXISTS BEYOND THIS POINT!
This is because the FMC didn't transition back to cruise phase. I'm betting the PM did not call the flaps either, as you extended them?
The CTD is essentially related to actual aircraft altitude, FCP selected altitude, and FMC computed ToC/ToD. To prevent CTD trap #1 and #2 (related) after the go-around, but BEFORE you attempt to do anything with the FMS, climb to your missed approach altitude. You will probably see a scratch pad message along the lines of CRUISE ALT 050 at this point. Level the aircraft, and the altitude at which you leveled off, make this the cruise altitude in the INIT page (e.g. if you are level at 4000 ft then enter 040). The very second you enter this you will hear a CLICK as the thrust rating changes from GA to CLB. At the same time the FMC transitions to CRZ phase.
Now you've avoided the CTD, you can re-program your approach. Don't climb too high, or select an altitude that is too high (if you stick to the distance rule of "3 times your altitude in 1000's of feet" you'll be OK). CTD bug #3 can hit you here, but as long as your altitudes remain sensible, there isn't a problem so don't worry. Once the approach is programmed, perform a DIR TO the first waypoint of the approach and fly as normal.
If you need to climb high (e.g. mountainous terrain) enter a waypoint that is not near the aircraft. Do NOT try and enter it at the FROM waypoint as this too will CTD!!!! To enter it successfully, press LEGS then enter it at LSK2L, and perform a DIR TO. Now you can do what you want around the airport if mountainous terrain is a problem. Before attempting to resume the flight plan, be sure to reset the cruise altitude to the current aircraft altitude. This will ensure the FMS sequences correctly when you perform a DIR TO the first waypoint on your approach (sometimes it is useful to re-program the STAR for the airport, especially in mountainous terrain).
Don't worry about the CTDs - they seem hard for some people to run into, or in my case, easy. The methods to avoid them are easy though.
Programming the FMS is fairly quick if you already know what you are programming in. You should be able to have the approach entered and sequenced correctly in less than 30 seconds (the aircraft will still be turning downwind on heading select by the time you prepared it).
Single crew operation is certainly busier, but it is by no means impossible.
This sounds suspiciously like the auto-throttle is still active (check to see if there is a box around the speed window - if NOT then it is *active*). You will need to assign two keys in PMDG Keyboard settings. One for auto-throttle disconnect, the other for autopilot disconnect.
Generally speaking, once the INIT page is programmed, you don't touch it again except for CRUISE and CI entries. To create a new destination, you press FPLNm then perform a LAT REV on the FROM waypoint at LSK1L. On the LAT REV page you will see the entry for NEW DEST. Enter the new destination in this box, and then press FPLN again.
You will see something like:
------- END OF FPLN
Now you are able to perform a LAT REV on KJFK and see the STARs for the airport! Configure the flight plan as normal, being aware of the CTD traps outlined above.