I do not know the diameter of your coin for certain, but by a process of elimination it appears that it should be in the neighborhood of 23-24mm, or 16-18mm.
If the larger, it is from the second group of bronze coinage from Cyzicus, first series dated 348-350. In that case, your coin is an AE2 (called a "Centenionalis") corresponding to RIC VIII #65 for the mint at Cyzicus.
If it is the smaller, it is from the third group, second series dated 351-354. In that case your coin is an AE3 corresponding to RIC VIII #104 with a pearl diadem.
The larger coin is much more rare than the smaller. BTW the emperor on the obverse was named after his grandfather and is Constantius II (two n only)
As for reporting the other coin, I will do that for you if you wish, but will have to refer any inquiries about details on to you. If I help you with that is that okay?