You have several codevio's here, and there's a better way to do it anyway.
You can retrofit a ground like you did, but you cannot retrofit just a neutral. The main reason is that all conductors must run through the same cable
or conduit, and currents must be equal in each cable: power must go back the way it came. This is because it is AC power: it will induce eddy currents (turn metal things into transformer cores, heating them up), induce vibration which damages cables, and produce lots of EMF radiation (which is normally very low because we follow that rule).
Proper wiring methods (NEC Chapter 3) must be used. It's not allowed to simply toss a single THHN wire alongside an existing Romex because THHN isn't listed to be installed that way. Even worse would be using one strand torn out of Romex, since that lacks its protective sheath, and isn't even labeled. You can't use random unlabeled wires.
1 wire per lug*. For one thing, it interferes with setting the correct torque - yes, that matters.
You can't run a new cable from lamp to switch? OK, but you can run a neutral wire from service panel to switch. How about a whole Romex cable? Run a Romex /2 cable from the service panel to the switch. Change the wiring from a switch loop, to a power-to-switch arrangement. Then, up in the lamp, cap off the power supply that goes to it, so it is fed from the switch.
Now your switch has always-hot and neutral from the panel, and neutral and switched-hot off to the lamp. Done!
House wiring uses a tree topology. You usually see it as more of a vine topology, but that's not required. You can have branches anywhere, including 6 inches from the circuit breaker. Yes, you can wire-nut in a service panel. And you can use stripped down Romex for a 6-12" pigtail. (the markings are every 12" anyway).
So you take your existing circuit's cable, and this new cable you just added. Join its two hots to a black pigtail with a wire nut; that goes to the breaker. Join the two neutrals to a white pigtail; that goes to the neutral bar or the GFCI/AFCI breaker. Now you're safe and legal.
Another way is to use a smart-switch/dimmer/whatever you are installing that needs neutral, take it back to Home Depot, and get a similar thing that does not need neutral. We're starting to see models appear on the market that do all the smart-switch things, require ground and not neutral, and UL is approving these, so there you go.
* unless the panel is rated/listed/labeled for 2 wires per lug (e.g. Pushmatics are, but they use screws not lugs).