I'm a veteran of many hurricane-season work stints int BVI (rode out 2 separate Cat 3s). Normally, we would be headed down there in 2 weeks, but the USVI and the BVI are in a disaster state right now after direct Category 5 and 4 hits, with a lot of the residents gone or trying to leave, problems with fresh water and food for remaining residents (never mind electricity), most infrastructure damaged or destroyed, and civil unrest causing security issues.
Now, Puerto Rico has much more robust civil infrastructure, police force, etc. Also, some parts of the island are likely to be much harder hit than others. However, if the situation ends up as bad there as the Virgin Islands, it'll be several months minimum before I would even consider venturing down there unless you absolutely must.
As to airlines, American has never outright refunded tickets to us, but we've never asked. The airport is usually one of the first things they try to open so that emergency relief can come in and people can be evacuated. Chances are you will be on the hook for the ticket. However, you can probably transfer the ticket for a fee of a 100-200$.
Good luck.