If you own a business you have to file a yearly return with the IRS regardless of whether there was a loss or profit.
To answer your question about your mom's tax return, the IRS lets you choose which way you want to handle it. You can file your own 1040 with your LLC's losses, or you can choose to let your mom claim you as a dependent on her tax return. However, you cannot do both. For example, when I was in college I worked in several paid internships and work study programs. My dad could have claimed me as a dependent, but instead I filed my own 1040 since he was no longer supporting me.
You and your mom (and possibly an accountant) need to decide which option makes more sense for you. If you had income from other sources it might make sense for you to file your own tax return. However, if you don't have any income to offset your LLC's losses, then it might be a better option if your mom claims you as a dependent.
I don't know how the LLC's losses will pass-through if your mom claims you as a dependent, since technically it's not her business. I'm not sure if she can claim your losses on her return, but she can at least claim the deduction for you as a dependent. You'll need to consult an accountant to figure out if you can get both.