We make use of APOGEE and $Gaia$ data to identify stars that are consistent with being born in the same association or star cluster as the Sun. We limit our analysis to stars that match solar abundances within their uncertainties, as they could have formed from the same Giant Molecular Cloud (GMC) as the Sun... We constrain the range of orbital actions that solar siblings can have with a suite of simulations of solar birth clusters evolved in static and time-dependent tidal fields. The static components of each galaxy model are the bulge, disk, and halo, while the various time-dependent components include a bar, spiral arms, and GMCs. In galaxy models without GMCs, simulated solar siblings all have $J_R < 122$ km $\rm s^{-1}$ kpc, $990 < L_z < 1986$ km $\rm s^{-1}$ kpc, and $0.15 < J_z < 0.58$ km $\rm s^{-1}$ kpc. Given the actions of stars in APOGEE and $Gaia$, we find 104 stars that fall within this range. One candidate in particular, Solar Sibling 1, has both chemistry and actions similar enough to the solar values that strong interactions with the bar or spiral arms are not required for it to be dynamically associated with the Sun. Adding GMCs to the potential can eject solar siblings out of the plane of the disk and increase their $J_z$, resulting in a final candidate list of 296 stars. The entire suite of simulations indicate that solar siblings should have $J_R < 122$ km $\rm s^{-1}$ kpc, $353 < L_z < 2110$ km $\rm s^{-1}$ kpc, and $J_z < 0.8$ km $\rm s^{-1}$ kpc. Given these criteria, it is most likely that the association or cluster that the Sun was born in has reached dissolution and is not the commonly cited open cluster M67. (read more)