I'm scared.

My mom moved away from her home and rented it to someone else and now I need to shift the delivery address to my apartment....
Crap..
What do I do.

can you get a mail re-direction?
I would set up a mail redirection, and also talk to whoever she rented it to, leave them your number and ask them to call you if they receive any packages with your name. Mail redirections are not 100% accurate.
Also, unless you were planning on assembling the chips yourself, you are probably having the chips shipped to an assembler. If that's the case, contact the assembler and just have them change the shipping address (as far as I'm aware, all of the assemblers are responsive right now).