AFCI randomly tripping, and related questions
AFCI
AFCI generally detects problems with wiring, but can be triggered by certain devices that may or may not be a dangerous situation. The more devices, receptacles, wire connections, etc., the more likely that (a) real problems will crop up that are actually being protected by the AFCI and (b) false &quot;nuisance&quot; trips will happen. But until you know for sure, you should assume the trips are &quot;real&quot;.
Do you need AFCI? Probably, but depends on location. Unlike GFCI, which is life-safety based such that out-of-reach (e.g., lighting) is normally exempt), AFCI is fire-safety based so lighting is as in need of protection as anything else, subject to local code requirements.
Pigtail
You can connect two circuits to one breaker. You use a pigtail to connect to the breaker on one end and the two separate circuits on the other end (pigtail plus the other 2 wires in a wire nut). However, that doesn't really gain anything here since your total current is limited by the neutral wire, unless you go to an MWBC.
Multi Wire Branch Circuit - MWBC
What you have described as a solution is a MWBC. Basically you have two hots and one neutral == /3 cable - connecting to two breakers. There are a number of catches to this:

The breakers must be on opposite legs. Traditionally that has been easy to do. However, if you were thinking of &quot;replace a full size breaker with a double-stuff pair of 1/2 size breakers&quot;, that won't work here because that would be on only one leg. There are, for some panels, quad 1/2 size breakers where one of the pairs can be used this way, but that is very panel dependent. The simple way to look at it is: If installed correctly, red to black will measure 240V, red to white (neutral) 120V, black to white 120V. If you get red to black 0V then everything is on one leg == NO GOOD.
The breakers must have a common maintenance shutoff because otherwise neutral current could be quite dangerous when working on 1/2 the circuit when the other 1/2 is off.
AFCI and GFCI get messy unless handled as part of the breaker.

Note that an MWBC is not &quot;two separate circuits&quot;. It is one multi-wire combined circuit. Effectively two circuits in one, but the savings being 3 wires (plus ground) instead of 2. Neutral &quot;cancels out&quot; which is why it works in general but also why it must be on a properly installed double breaker.
Two truly separate circuits would require 4 wires (plus grounds) - i.e., each circuit needs its own paired hot &amp; neutral. An MWBC shares the neutral in a safe way.