Heat transfer between baryons and millicharged dark matter has been invoked as a possible explanation for the anomalous 21-cm absorption signal seen by EDGES. Prior work has shown that the solution requires that millicharged particles make up only a fraction (mχ/MeV )0.0115 %≲f ≲0.4 % of the dark matter and that their mass mχ and charge qχ have values 0.1 ≲(mχ/MeV )≲10 and 10-6≲(qχ/e )≲10-4 . Here we show that such particles come into chemical equilibrium before recombination, and so are subject to a constraint on the effective number Neff of relativistic degrees of freedom, which we update using Planck 2018 data. We moreover determine the precise relic abundance f that results for a given mass mχ and charge qχ and incorporate this abundance into the constraints on the millicharged-dark-matter solution to the EDGES signal. With these two results, the solution is ruled out if the relic abundance is set by freeze-out.