No. No. No…
NEVER open another credit card or any other new line of credit 6 months prior to applying for a mortgage, and especially not a secured credit card (they are for people with bad or no credit history). Opening a new line of credit will only lower your score, and it will take you 6 months to level off again.
Increasing the limit on any of your existing credit cards as suggested below won’t help either, because you carry no balances. Your utilization is 0% anyway, and having a higher credit limit won’t improve that. It can only help if your utilization is higher than 30%.
Having a month to raise your score by 15 points is almost impossible. The only thing that can do this is good stream of timely payments, but that would take a couple of months. Each time you make a timely payment, your score inches up a bit. 16 points is just too much of an increase to achieve in just one month.