From your pictures and description I cannot tell where your fuel leak is.
If it is in the area of in front of and inside of the drivers rear tire, you probably have the semi-common problem of rotted fuel lines. There is no factory recalls for this, so you are on your own to repair it.
If it is toward the passenger side and dripping from the fuel tank skid plate, you may be in luck and qualify for this recall # 12191B. Also a fairly common Cobalt problem.
https://testing-public.carmd.com/Tsb/Download/109096/4233868
And if you are leaking at the filler neck where it enters the fuel tank, the plastic nipple not the rubber hose, another problem but less common, you may qualify for factory replacement, but there are no longer any factory gas tank in inventory, so you May be S.O.L.
About the only option is scrap yard used gas tanks, you pays your money and takes your chances there.
If you take you car to the dealer to determine the problem,and it turns out to be a repair not covered by a recall, be prepared to call the police to Get your car out of the dealer they may try to soak you for a $1K+ repair bill and say it is illegal to let you take your car because it is unsafe. Call their bluff and call the police yourself.