I want to know if I can drop the light crossbow because I'm playing as an Artificer, and I don't really need it?
Yes, you can drop your crossbow.
The "How to Play" section of the introduction to the Player's Handbook has three rules for how to play the game.
1. The DM describes the environment.
So your DM might say, "You have a crossbow".
2. The players describe what they want to do.
Here, you would say "I drop my crossbow."
3. The DM narrates the results of the adventurer's actions.
The DM would then say something like, "Okay, there is a crossbow on the ground."
Maybe try to sell it next time you're at market.
Its probably a better idea to try to sell it if you don't want it, light crossbows have some value, coming in at 25gp.
But it may be better to have and not need.
Alternatively, if you've got the carry weight to spare, just hand on to it. You never know when you will need to take a shot from 320 feet away, or if one of your friends may be able to make use of it.
You are not, of course, required to hold onto all the gear your class starts with. If you want to sell your crossbow, leave it in your apartment, or just throw it away to save weight, go for it. It's up to you to do things like that. The DM will help you figure out what to do if you decide you want to sell it, but in general weapons can be sold for half their list price, so you could expect to get about 12 gold for a light crossbow.
Alternatively, you can fully customize your starting equipment. As the Artificer Starting Equipment section specifies,
If you forgo this starting equipment, as well as the items offered by your background, you start with 5d4 x 10 gp to buy your equipment.
Usually you get a better deal by taking the starting equipment package, but if you want a very different loadout than you're offered or want to take a gamble on the dice roll, it can be a good choice.