Cold water sour taste
Here is an educated guess: firstly the typical dental anesthetic is lidocaine which tastes very bitter. Secondly, a bitter taste if often misclassified as sour. Thirdly, sensory thresholds (the amount of a compound required to detect its taste) is temperature dependent and lower at cooler temperatures. In other words, I assume that drinking cold water made you able to detect small remaining traces of bitter lidocaine that were too small to detect at warmer temperatures, and that you misclassified as sour.

Wei, Y., Nedley, M. P., Bhaduri, S. B., Bredzinski, X., &amp; Boddu, S. H. (2015). Masking the bitter taste of injectable lidocaine HCl formulation for dental procedures. AAPS PharmSciTech, 16(2), 455-465.

https://www.sensorysociety.org/knowledge/sspwiki/Pages/Sour-Bitter%20Confusion.aspx

McBurney, D. H., Collings, V. B., &amp; Glanz, L. M. (1973). Temperature dependence of human taste responses. Physiology &amp; Behavior, 11(1), 89-94.