No, I have not ever used or purchased a door lock for a hotel room. Usually they have that swing bar that goes over a knob and we use that in addition to the deadbolt lock. I hope that you don't have to use an extra lock but if it makes you feel more secure, it would be worth it to you.
I suppose you could also place a chair and/or your luggage in front of the door so someone on the outside would have to try really hard to push it away? If, by then you are in that situation, it would probably be too late. Not to try to make you panic or anything but I think you'll be fine. Why do you think its too late to cancel your hotel? Have you prepaid it? If you haven't pre-paid it, you can cancel it and book somewhere else.
If you have pre-paid, then just being careful and keeping a watchful eye should be good. Just as a side note, doing this in all cities is a good idea, not just San Juan.