Call the county health department; it is possible they will test for coliform and nitrates for free. We lived on a shallow, hand-dug well like that for several years, and our biggest risk was not septic tanks but agriculture -- potential for coliform from neighboring cow pastures and nitrates from fertilizer on soybean fields just a little further off. The question is how the groundwater runs.
If the testing is too expensive for now, wash only clothes, not dishes, in the water.
Or, even better, shock the well with bleach. The Heath department or the extension office will tell you how much to use now that you have the well"s dimensions to give them. You might tell them an animal fell in, not that you can't afford to test for now. You dump in bleach, wait, then run the water until you can't smell bleach. If you're worried about talking to the heath department, just dump in an overkill of bleach (a full gallon would likely do), but then it would be best for your septic tank to run an outside hose for a while rather than putting that much bleach down the drain. The advantage of this is bleach is dirt cheap.
At that point, you should be able to wash dishes for a while without getting cholera, though I still wouldn't cook with it or drink it.
If no one has told you, you can't just boil the water to make it safe, because boiling will only concentrate nitrates, which by themselves are very bad for you. The risk for blue baby syndrome actually comes from nitrites, not nitrates, but nitrates can break down into nitrites, so where there's one, the other is very likely present.
Look for a pm from me.