In very cold water bodies remain well preserved for days to weeks, in which case there is a good chance of determining the cause of death.
If there are no wounds on the body, and autopsy did not reveal a cause of death, and there was no significant natural disease that could explain death, then the cause of death could well be drowning.
It is a myth that drowning causes water in the lungs. In fact, dying from any cause, there is often the formation of pulmonary edema (backup of fluid into the lungs from heart failure), but this is different from gross water in the lungs. In some drowning cases there is spasm of the upper airway as soon as water contacts these structures, and actual water never enters the lungs.
As in other deaths, drowning deaths may produce pulmonary edema. In fact, extensive pulmonary edema with abundant frothy white foamy fluid in the nasal passages, larynx and bronchi is a characteristic finding in drowning, especially fresh water drowning. Nevertheless, after several weeks in the water, the body of a drowning victim may no longer show this finding.
One petechial hemorrhage in the eye area is of little significance. It would not indicate injection into the eye. It is simply not reasonably possible to kill someone by injecting a substance into the eye. There is no space in the eye to hold any significant quantity of injected material. If such injection were attempted, the eye might rupture, yielding an autopsy finding much more dramatic than a single petechial hemorrhage. Also, if the subject is conscious and not in an overdose situation, even though intoxicated (I presume the alcohol level you referred to was 0.17 Gram Percent), there would be no way to inject his eye without marks and wounds due to extreme struggle.
Finally, if your question were based on a real event, then the coroner/medical examiner office in the jurisdiction in which the body was found would have investigated the case. Surely an autopsy would have been done, along with toxicology studies. The records of the investigation, autopsy and toxicology are public, and available to you for a nominal fee.