Usually sports drinks with electrolytes are made for athletes since they are constantly sweating but with cases where people simply don't absorb liquids and nutrients well they can also be beneficial. So its something to try for now.
One thing that would also be a good idea if your specialist is willing or a regular doctor is to have blood work done and check all of your vitamin levels like B12, Iron, Vit D, A, C, Calcium, D, folic acid, potassium etc. to make sure you aren't low in any of them and if you are then you can try supplementing them then have it tested again (maybe a month or more later) to see if the supplements are working. Even if you aren't deficient you can still feel the affects of a deficiency if you are low. Normal range is best. Being low or deficient can make you feel dizzy, tired, faint along with a plethora of other undesirable symptoms.
While you're seeing your regular doctor you can have them run tests to see if there's any other underlying cause for the low blood pressure in case it isn't just the heat and humidity. For me I have heart problems and I tend to have a lower blood pressure and do take a beta blocker to keep it from dropping too low. Hopefully its just a hydration issue though. Do your best and keep us posted.