There is no short-term fix for rebuilding credit, especially not by January. Any action taken here has to be for the long-term, and will almost certainly conflict with actual, good financial advice. Getting a credit card and paying it off monthly can be a wise move from a financial standpoint, but it will not build credit as solidly as having a revolving balance that you make payments on. Reason? Credit scores are NOT just a reflection of your ability and willingness to repay a financial obligation. Another, somewhat hidden component to a credit score is your PROFITABILITY to a potential lender. This is a system that was designed for and by lenders, and their primary goal is to make as much profit as possible for the least amount of risk. Those two pieces go hand in hand. In my opinion, this is your least important consideration right now and I would recommend not even bothering with this for the next year or two.

Your most important consideration right now is short-term survival. If your current domestic situation does not involve kids, this is significantly easier. Consider renting a room instead of an apartment. Renting a room sucks, we all know that. Roommates suck. They just do. But this may be a necessary evil and will likely be significantly cheaper than the apartment option. Plus you are renting from a person, not a corporation, so credit check may not be as much of a factor (or more easily explainable). If you have kids, this is going to be a lot harder, but not impossible... For example, maybe you can rent a whole basement out from someone. A little more pricey, but look on craigslist you never know what you can run into.