It is entirely possible it is oil, however the presence of oil in an aquifer does not imply there is a suitable trap.
Oil (so the current theory goes) is generated in shales and general gunky slime laid down under anerobic conditions (no oxygen). The slime and gunk is buried and compacted and movered around and hopefully heated up. If the rock ( known as source rock) is buried under the right conditions the organic matter will be cooked up into an nice healthy hydrocarbon mixture.
This will them migrate upwards following what ever path it can through permeable rocks.
If you are lucky it will enter into a formation which is porus - sandstone and limestone formations are typical. But not only does it need to be porus, it must have a seal that prevents the oil moving on up. Examples of a seal would be a imperameable shale cap rock, a sealed fault boundry or a salt layer.
(oddly enough the seal rock for most of the north sea oil is the kimmeridge clay, which is also the source rock. The source rock ends up above the reservoir and becomes the seal due to all maner of faulting and rocks being thrown up and down).
(should you be in the UK and go down to kimmeridge bay in the south coast, the kimmeridge clay is at surface, it smells bad.)
If there is no seal then the oil will keep moving until it exits. If it does hit a seal , you may well get an oil accumulation and mr and mrs hillbilly can place an order for that ferrari assuming the accumulation is worth while, the cost of drilling down to the reservoir is acceptable and the permeability of the reservoir will allow production rates to recoup the upfront investment before the interest rates kill you.
If what you have in your water is oil and is not contamination from somewhere else, then there is indications you have a source rock feeding the area.
The problem is finding a good trap. As mentioned by others above, the early oil fields in the US and azerbaijan were indictated by large accumulations at surface, so there certainly was a healthy source rock feeding the area, there were also local shallow traps. Hand dug pits , water skimming and shallow (75m) wells were all that was needed to extract it. Note these were source bubbling to surface, no a mild sheen in the water.
On another tangent - if you go and visit the mud volcanos just south of Baku, you will see cold water bubbling to surface with a sheen of oil. The caspian basin reservoirs that are left (and tehy are blinking huge) are mostly to be found offshore under some fairly challanging conditions to get to. The point of this tangtent is that there may be oil moving up , but it also moves laterally along the dip of the formations, so oil at point x may have moved form ponit y 150 km away.
In your case, the question remains - can you find a good sealed trap - and will it be large enough. Take a look around - are the rocks fairly well broken up, lots of ridges etc etc? As you are looking at oil which is already failrly shallow (I assume your well is not more than 100m deep) then you have to determine the possiblility of a formation with no natural faults/fissures and a good seal between you and the bottom of the well. My geuss would be that it is unlikley.
It is not an unusual occurance for oil to be produced but subsequently lost. I was working through a recent mass balance study of a reservoir basin. There were 2 good source formations, which had been cooked under the right conditions and a shallow marine environment had left large salt layers above for a good seal. Alas tectonics got in the way several million years back and heavily faulted and fractured the area and threw up a hill range as a by product. End result, a geustimate would be 97% of the hydorcarbons produced never found a good trap as the ground was folder and shifted around after they were produced. (the remain 3% is still a multi Tcf gas basin, but hey ho). IRRC Destin dome offshore florida was another area where the source rock was good, alas the reservoir and seal formed several million years too late.
So in short - if you have oil moving through, don’t get too hopeful, no sizable trap then no worthwhile accumulations. If you have a spare 10million to fund a drilling campaign, my advice would be to take it to vegas, you will get better odds.
On the contamination front, if you are up dip of a salt storgae for LPG or oil, these salt cavern have been known to crack and leak into acquifers. Do not under estimate how far this crap can travel. If you do nothing else, get it sampled, your best chance of getting rich is suing someone for groundwater contamination.
for the record I am involved in the oil industry exploration side of affairs which may or may not lend the above waffle with some credibility. Or not.