Can you be added to someone else's checking account if you can't get one of your own?

Yes, with that persons permission and signature. You both would have to go to the bank and have you added and how it is listed on the account will also determine how the moneys can be drawn or written. If you get an account that says Sally and Bob both of you would have to sign for every check and withdrawl. If you get one that say Sally or Bob then either of you can make transactions. Ask the bank what the best way to set it up will be for the type of usage you will have.