Lung injury? Have you recieved medical clearance to dive? You need to check with a dive physician, depending on the lung injury. Your greatest difference in pressure is in your first ATA, so it really doesn't matter if you shallow dive with a lung injury. Let's say you had a punctured lung, it healed, you feel fine, but when you decend 1 ATA your lungs decrease in size by 1/2 but when you breath they expand fully. You have a weakened area in your lung and the change of reoccurrance of injury is great, especially if you see something, get excited, hyperventilate or worse yet hold your breath and unknownly ascend...pop goes the lung again! Definitely get a physicians clearance first.
Ok, now the preaching as a re-compression chamber nurse is over, $1,000.00 for the winter for a month is not much for either Belize or Bonaire. That is limiting yourself to just of $33.00 a day and you are talking high season. You can't even get a room for that. Now if you have a buddy who is going with you and you both have $1,000.00 for a month, it might be doable. Remember winter is high season for both areas and prices can be quite expensive. Even if you exclude the room and airfare, diving will cost you, including food. On Bonaire you can get food rather inexpensively at local snacks or you could consider shopping and cooking in if you get an efficiency apt. Best of luck!