Automatic modulation recognition (AMR) is an integral part of an intelligent transceiver for future underwater optical wireless communications (UOWC). In this paper, an orthogonal frequency division multiplexing (OFDM) based progressive growth meta-learning (PGML) AMR scheme is proposed and analyzed over UOWC turbulence channels. The novel PGML few-shot AMR framework, mainly suffering from the severe underwater environments, can achieve fast self-learning for new tasks with less training time and data. In the PGML algorithm, the few-shot classifier, which works in the presence of Poisson noise, is fed with constellations of noisy signals in bad signal-to-noise ratio (SNR) scenarios directly. Moreover, the data augmentation (DA) operation is adopted to mitigate the impact of light-emitting diode (LED) distortion, yielding further classification accuracy improvements. Simulation results demonstrate that the proposed PGML scheme outperforms the classical meta-learning (ML) approach in training efficiency, robustness against Poisson noise and generalization performance on a new task.