  Motivated by recent experiments that reveal expansive fractional quantum Hall
states in the $n=1$ graphene Landau level and suggest a nontrivial role of the
spin degree of freedom [Amet {\em et al.}, Nat. Common. {\bf 6}, 5838 (2014)],
we perform accurate quantitative study of the the competition between
fractional quantum Hall states with different spin polarizations. We find that
the fractional quantum Hall effect is well described in terms of composite
fermions, but the spin physics is qualitatively different from that in the
$n=0$ Landau level. In particular, for the states at filling factors $n/(2n\pm
1)$, both exact diagonalization and the composite fermion theory show that the
ground state is fully spin polarized and supports a robust spin wave mode even
in the limit of vanishing Zeeman coupling. Thus, even though composite fermions
are formed, a mean field description that treats them as weakly interacting
particles breaks down, and the exchange interaction between them is strong
enough to cause a qualitative change in the behavior by inducing full spin
polarization. We also verify that the fully spin polarized composite fermion
Fermi sea has lower energy than the paired Pfaffian state at the relevant half
fillings in the $n=1$ graphene Landau level, indicating a lack of fractional
quantum Hall effect at half filling in the $n=1$ graphene Landau level.
