Ok, so according to everything I've looked up you should be able to get married again after killing your spouse in Skyrim but I'm wearing the amulet of Mara and no one will give the dialogue options when I talk to them. Is this a glitch? Do I need to do something else?
According to the highest voted answer here marriage is forever and it is not possible to remarry after your spouse's death. According to answers on this similar question, remarriage might not be possible due to a bug.
If a spouse is killed, it was intended that the player be allowed to remarry but the command to restart RelationshipMarriage was never added to RelationshipMarriageFIN. (Bug #14856)