I suffer from high blood pressure and must take medications in the form of pills for my condition every twelve hours. Would it break my fast if I swallow a pill without water or anything else and continue fasting?

Swallowing pills vitiates fasting. If you cannot fast and you are in need for your medicine during the daylight hours of Ramadan, it is permissible for you to take the dispensation to refrain from fasting.
And God Almighty knows best.