Biomedical entity linking, also known as biomedical concept normalization, has recently witnessed the rise to prominence of zero-shot contrastive models. However, the pre-training material used for these models has, until now, largely consisted of specialist biomedical content such as MIMIC-III clinical notes (Johnson et al., 2016) and PubMed papers (Sayers et al., 2021; Gao et al., 2020). While the resulting in-domain models have shown promising results for many biomedical tasks, adverse drug event normalization on social media texts has so far remained challenging for them (Portelli et al., 2022). In this paper, we propose a new approach for adverse drug event normalization on social media relying on general-purpose model initialization via BioLORD (Remy et al., 2022) and a semantic-text-similarity fine-tuning named STS. Our experimental results on several social media datasets demonstrate the effectiveness of our proposed approach, by achieving state-of-the-art performance. Based on its strong performance across all the tested datasets, we believe this work could emerge as a turning point for the task of adverse drug event normalization on social media and has the potential to serve as a benchmark for future research in the field.