Brief Answer:
Endocrine

Detailed Answer:
Sorry to learn about your dry mouth and thirst.

There can be quite a few causes for this. It requires a systematic evaluation and physical examination which is possible only in person. So I urge you to get checked by an internist/endocrinologist.

Some medications can result in dry mouth. But it appears you are no medications.

Then there are some endocrine (hormone related) reasons we can consider here:

1 Uncontrolled diabetes

Your glucose was 138 recently. Now although it is just one reading, one gets the impression that your diabetes is not poorly controlled. However to be certain, some tests are required such as
Frequent self monitoring with a glucose meter
HbA1c (a random blood test done at a laboratory which gives the previous 3 months' glucose average)

2 Diabetes Insipidus
This is a completely different type of diabetes in which the affected person is constantly thirsty and drinking water, also is passing large amounts of urine.
This diagnosis requires special testing called Water Deprivation test, which also requires a special medication called ADH (also called Vasopressin)

This specialised testing is performed typically by an endocrinologist.

3 General tests
When I see someone like you in my practice I order the following tests as well :

CBC
Electrolytes
Calcium
Kidney function tests
Liver function tests
TSH
Free T4

Further testing (such as Prolactin, Serum Cortisol, FSH, LH and Estradiol) can be considered based findings on physical examination and results of preliminary rounds of tests

---