I realize it's probably a bit late for this, but there really isn't enough info here to know exactly what is going on. Hyacinth grows from a bulb that is planted in the fall. It blooms in spring, and after it is finished blooming the leaves turn yellow and die off. The bulb will go dormant until next year.
If your hyacinth was in a pot and purchased 'forced' in a nursery, those plants are treated as annuals and usually disposed of after bloom. You can plant it outside if you like. They often won't bloom again, but if it does, it won't look like the one you purchased as it won't have a full flower stalk.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.