Allergies can cause all kinds of reactions... including retaining extra fluids that could result in HBP so yes, it is possible. Gluten intolerance is much more prevalent than most research suggests so you might wish to get checked out... unless our question means you already now this allergy or intolerance exists.

Sometimes it can take a while before diuretics really kick in and in some cases you may need to take more than you are. I'm not a big fan of meds but they are sometimes necessary for the short term.

The fact that your symptoms worsen when you increase carbs definitely indicates a reaction or allergy to something. A good way to detect the culprit is to eliminate all possible offending foods from your diet for two weeks and then slowly add them back in one at a time. As you add one back in, check your reactions/symptoms. If they increase, you've probably found your offending food type. Also check for redness on the top half of your ears within an hour after eating. This can be a common allergic reaction as well.