Dilation and thermopower measurements on YbAgGe, a heavy-fermion antiferromagnet, clarify and refine the magnetic-field temperature (H-T) phase diagram and reveal a field-induced phase with T-linear resistivity. On the low-H side of this phase we find evidence for a first-order transition and suggest that YbAgGe at 4.5 T may be close to a quantum critical end point. On the high-H side our results are consistent with a second-order transition suppressed to a quantum critical point near 7.2 T. We discuss these results in light of global phase diagrams proposed for Kondo lattice systems.