Looking at the list of compact states, neither Alabama nor Louisiana are listed. You should be able to obtain the new license by endorsement & still maintain your original license. Check with both Boards of Nursing just to make sure.
Re:the nurse licensure compact, there are several states (AK?,AZ,CO,DE?ID?,IO?,KY?,MD,ME?,MS,NB?,NC,ND,NH,N M,SC,SD,TN,TX,UT,VA,WS?) that allow practice with one license. You have to declare a home state/state of residency then you are granted practice privileges in the other compact states. There is more info at www.ncsbn.org/nlc.htm