Healing Spells......
Guild Wars 2 utilises skill queueing, i.e. hitting (default) keybinds 2 then 6 in rapid succession will cause your character to use skills #2 and #6 one after the other.
The cool-down will appear for like say 2-3 seconds be-for you can re-use it (considering it didn’t even work but then it may work/may not & do the previous 2-3 seconds)
Most, if not all, healing skills have a cast time. Hence by your description, you seem to be interrupting the skill or it is being interrupted by the enemy, causing a mandatory 3 second cooldown.