The N'EX is a rather complex service. Some trains operate as a single through service, while other trains have two origin points and then meet at Tokyo station for the continuing journey as a longer train to Narita airport.

JR-EAST Train Reservation

This is the timetable for the Narita Express service. Look up your train departure from Tokyo station and see if there are two trains that depart Tokyo station at the exact same time with the same train number.

Example: Narita Express train number 33 has two parts. One part of this train departs Yokohama at 13:59, stopping at Shinagawa at 14:20. The other half of this same train departs Shinjuku at 14:10. At Tokyo station, the two parts of this train connect together, and the train continues to Narita airport. By the way, it is not possible to walk from one half of the train to the other half - the "engine" is in the middle once the two separate trains are joined at Tokyo station.

The problem obviously is that Narita Express is a reserved train. You have a seat departing Tokyo station, but it MIGHT be a seat that is on the half of the train that originates at Shinjuku (not stopping at Shinagawa) and not the half of the train which originates Yokohama (which does stop at Shinagawa).

Please note. I agree completely - Tokyo station is a bad place to change trains from Shinkansen to Narita Express (it's a long walk from the Shinkansen platforms above ground to the N'EX platforms in one of the sub-basements of Tokyo station). Shinagawa is a much better place to change from Shinkansen to N'EX.

Be sure to look up your train in the timetable and see if you might have lucked out and be booked on one of the N'EX trains which don't split/join at Tokyo station.

EDIT: N'EX train number 17 is one of the few that does not split. It departs Shinagawa at 10:23 and Tokyo at 10:33. Looks like OP will be just fine getting on at Shinagawa!