While each property appraiser office is different in regards to the turn around time for getting new information input, it is not uncommon for it to take 2-3 months. Keep an eye on it, but don't worry about it.
In Broward county it usually takes up to few weeks. If after few weeks, you won't see the names of new owners appearing in the public records, you may try to contact Broward County appraiser's office and ask. But at this point, you should not worry.
It depends a lot on the County recorder's office and the speed with which they are processing files. I have seen it take up to 6 months for the records to be updated. It doesn't affect the fact that you have sold your property and you are no longer "in title" to it (so long as the deed was, in fact delivered to the Buyer and recorded in the public records).