Jamaica doesn't have a working postal service like the US. You can't mail a letter from one parish to the next because residential addresses are not tracked or used by anyone except delivery drivers and workmen. The few Jamaica Post locations that I have seen looked like ghost towns. And there is no Federal guarantee that your mail won't be tampered with or read.
If you want your US mail you must have it forwarded to a friend or relative living in the States. It will never physically cross the ocean.
In order to get a package from the US you have to use a Jamaican shipping service with a PO box in Florida. Then you pay customs fees, you pay a fee based on the item's weight, and also a delivery fee, sometimes the total fees you end up paying equal the item's cost, so you pay twice for whatever you ordered.
If you purchase an item from Amazon and it only takes one day to be delivered to that US PO box it may then take one to three weeks to get to your Jamaican address, because local delivery drivers try to group their assignments together.
EDIT: And don't ever put your money in a local bank, the bank employee you just dealt with might embezzle from your account, or they will just arrange to have you physically robbed.