You don't say why the police say they're looking for your boyfriend. So, just from your question, it seems possible that they want him for anything from missed child support payments to murder. Any attorney with any experience with the police or the criminal justice system would strongly advise you to CONSULT WITH A CRIMINAL ATTORNEY RIGHT AWAY. Without knowing it, you could be in jeopardy yourself, for example, on a harboring a fugitive charge.
To answer your more specific question: No, unless they have a warrant to arrest your boyfriend that lists your home as his address, too, or unless they have a search warrant for your house, it seems very unlikely that they have any right to demand entrance. But they can always ask you to let them in. And if you agree, then you are surrendering your right to keep them out. The general advice I'd give in this kind of situation -- and I stress that I don't know the specifics of yours -- is to say clearly that the police do not have your permission to enter. On the other hand, it would be foolish and dangerous to resist them physically, if they insist on coming in after you've clearly denied them permission.
But I come back to the point that you should consult with a criminal attorney, who can advise you more specifically and possibly help resolve the situation. (I also cannot advise you specifically on FL law; I'm licensed in MD and DC.)
You absolutely do not have to let the cop into your home unless he has a warrant. If he threatens to get a warrant then you should still refuse to let him into your home until he comes back with an actual warrant. You don't even have to open the door for the cop when he knocks, just like how you don't have to open the door for anyone else.
This is not to be considered legal advice nor does an attorney-client relationship exist.