Bats in India can carry rabies, so I never dismiss bat contact casually. But rabies needs saliva entering a bite, scratch or broken skin or a mucous membrane - brief touch on intact skin, or a bat sitting on your shirt, does not transmit it. You saw no bite, no scratch, no blood, and 16 days have passed with nothing, which is reassuring. Wash that finger area with soap and water anyway, and if you recall any scratch or open cut at that moment, take the vaccine series even now, since it is still worthwhile. Your GAD is amplifying this fear more than the actual risk - talk it through on a Practo consult with me and we will settle both the rabies question and the anxiety loop.
Next Steps
Wash the area with soap and water; no vaccine needed if skin was truly unbroken. If any scratch or open cut was present, start anti-rabies vaccination now and consult me for the schedule.