Biointegrated intracellular microlasers have emerged as an attractive and versatile tool in biophotonics. Different inorganic semiconductor materials have been used for the fabrication of such biocompatible microlasers but often operate at visible wavelengths ill-suited for imaging through tissue. Here, we report on whispering gallery mode microdisk lasers made from a range of GaInP/AlGaInP multi-quantum well structures with compositions tailored to red-shifted excitation and emission. The selected semiconductor alloys show minimal toxicity and allow the fabrication of lasers with stable single-mode emission in the NIR (675-720 nm) and sub-pJ thresholds. The microlasers operate in the first therapeutic window under direct excitation by a conventional diode laser and can also be pumped in the second therapeutic window using two-photon excitation at pulse energies compatible with standard multiphoton microscopy. Stable performance is observed under cell culturing conditions for 5 days without any device encapsulation. With their bio-optimized spectral characteristics, low lasing threshold, and compatibility with two-photon pumping, AlGaInP-based microlasers are ideally suited for novel cell tagging and in vivo sensing applications.