Your best bet is to retrace your steps from the beginning of the quest, or from the previous quest if there is one. 99.9%
There's no bug though, they changed how WS are counted for weaponskill quests; so you may not have gotten as much (or any, depending on the circumstances) credit as you thought.
You may wish to consult this information about WS points-
https://ffxiclopedia.fandom.com/wiki...n_Skill_Points
Make sure you are fighting enemies of sufficient level. They must not check Too Weak.
Avoid using style lock while doing weapon skill trials, it is known to cause issues, although you will still correctly accumulate points the completion may not be reflected while style locked.
If you threw the weapon away, you should be able to get another from the quest-giver; if that doesn't work you may need to use your one time item restore to recover it. General rule: Don't throw items like this away ever, even if you think something's broken.