Je fais de la pression>>>I have blood pressure. That is very nice, because without blood pressure you are dead. So what should it be: je fais la pression haute/basse? Or is the sentence all right and does it mean: I put on pressure? Francophones, allez-y!
It can mean to put political or emotional pressure on someone to carry out your wishes. Without more context there are so many possibilities.
Sure, but then is would be: "Je fais de la basse pression" (I have low blood pressure) or: "Je fais de la haute pression" (I have high blood pressure). From the fragment you have given it looks like: "Je fais de la pression [sur quelqu'un]".