That sounds like a symptom of severe renal dysfunction to me. Those symptoms occur when the kidneys are unable to excrete excess alkali, but healthy kidneys are able to excrete very large amounts of alkali without any problem at all (the blood is constantly attempting to keep its pH slightly basic at 7.35-7.45 against a variety of acid loads).
The only alternatives I can think of would be insufficient water intake or consumption of truly gargantuan amounts of sodium bicarbonate (which sounds unlikely).
Ironically, a steady intake of sodium bicarbonate at levels that don't give rise to too uncomfortable levels of hypertension (and avoiding muscle twitching as best as possible, of course) can actually greatly improve renal health long-term. The hypertension stems from the sodium causing more water to be retained, but sometimes this is exactly what you need, especially for kidney health due to how more water there can help a wide variety of issues. If you consider e.g. the analogy to water pipes, you want pressure to be high enough for the pipes to remain open and clear and for water to be delivered properly, but not so high that the pipes burst (in the body this would be analogous to ruptured vessels, and more dangerous conditions such as embolisms). You could even liken it to a more natural system of e.g. river flow, where you need sufficient flow in the river to keep the water clear and a fresh source for life downstream, whereas too little will quickly lead to stagnant and murky pond water, while too much will lead to flooding.
From personal experience, low blood pressure can feel just as bad, and even worse, than high blood pressure, and there's a lot of evidence from recent times that shows how too low blood pressure is just as much of a risk factor for disease as too high blood pressure. I typically have a very good intuition for what it feels like to have too high blood pressure, as it feels like the type of pulsating sensation you get from blood flowing to newly inflicted wounds, and of course try to avoid that, while simultaneously making sure that my blood pressure remains high enough as well.