The City of Boston lists housing lotteries on their Metrolist website, you can also sign up for email updates. I would also recommend viewing the Baystate Banner and the affordable housing online website. Metro Housing Boston also list affordable rentals.
No referral needed
Before you go into the shelter here are some helpful tips.
Most shelters have limited storage options. With membership, some fitness centers will allow you to rent lockers. Storage units outside of Boston are less expensive. Consider the hours of operation, and those on public transportation routes.
Carrying your social security card, or other delicate documents on your person is not recommended. Consider opening a safety deposit box your local bank. If you value it, secure it. Using small locks to secure the zipper on your backpack is also a measure you can take to protect your items.