Condoms work pretty well. They protect the areas that are covered. A condom would be effective against HPV in the throat as it is unlikely that your throat will be in contact with an uncovered area.
But there is no guarantee that lips and other areas are HPV free.
I wouldn't worry too much about it though. Oral HPV is rare, and giving a partner HPV through oral sex would also be rare, particularly if you warts have been treated.
No that might not help, because it could be in your lips and not know it. If you stay only in the area with the condom your safe though.