Re: urine home glucose and ketone tests
Random urine tests will not tell you enough. You only spill sugar and/or ketones in your urine if your blood sugar is extremely high. You could be way over normal range and still not spill sugar or ketones.
Best thing to do would be to buy a blood glucose meter...I believe some people have said that the WalMart brand is fairly inexpensive (although it will be more expensive than a vial of test strips.) Failing that, at least get the blood-testing strips (Chemstrips is one brand). Those will react to mild, moderate and large amounts of glucose in the blood...you still have to stick your finger.
I think you're quite smart to be concerned, given your family history and the amount of weight you gained. It is a lot better to stay on top of things and get treatment right away if you do turn out to be diabetic than to wait so long that you end up with permanent damage to something (nerves, heart, kidneys, etc.). Some people may come on here and tell you to "just watch your diet and exercise", and that's good advice, but given your other illness, it might not be possible for you to lose the weight you've gained. So do test, and make sure your doctor does both a fasting blood glucose and an A1c at least 2-3 times a year.