Hello, my suggestion would be to look for an Optical shop that advertises lens brands such as Zeiss, Rodenstock, Hoya or Essilor. They offer computerised facial measurements that ensure the correct placement of the reading portion of the lens. Sounds like you require a multi focal lens which does need you, your frame and the prescription. Other posters are correct, without the right training, the measurements taken will likely be wrong. By finding a place with the computerised option, it’s less likely to be incorrect. The downside is you’ll may be needing to purchase the lens design they have measured for which may be costly, but worth it in the end! The prescription done by an Optom or Ophthalmologist will not have any of the facial measurements, they are two distinct components to a prescription, but is preferable to the machine some places use to “test” your vision.
Two main facial measurements are called PD (pupil distance) and heights. Heights measure where the reading part of the lens will start from, the PD measures how wide apart your pupils are. Hope that helps. Good luck!