A dedicated reprocessing of satellite altimetry data from the Jason-1/2/3 missions in the world coastal zones provides a large set of virtual coastal stations where sea level time series and associated trends over 2002-2021 can be estimated. In the Gulf of Mexico, we obtain a set of 32 virtual coastal sites, well distributed along the Gulf coastlines, completing the tide gauge network with long-term data that is currently limited to the northern part of the Gulf. Altimetry-based coastal sea level time series and associated sea level trends confirm previous published results that report a strong acceleration in tide-gauge based sea level rise along the US coast of the Gulf of Mexico since the early 2010s. In addition, our study shows that this acceleration also takes place along the western and southern coasts of the Gulf of Mexico. The coastal sea level trends estimated over 2012-2021 amounts to ~10 mm/yr at most virtual stations. We note a slightly smaller rise on the western coast of Florida and at two sites of the Cuba Island. Good agreement in terms of sea level trends over 2002-2021 is found between coastal altimetry data and tide-gauge record corrected for vertical land motion. Good correlation is also found between coastal altimetry and tide gauge sea level time series at low-frequency time scales, with interannual fluctuations in sea level being indirectly linked to natural climate modes, in particular the El Nino Southern Oscillation (ENSO).