It still could take a little time. I started from zero with a touch of bad but mostly no credit. I got a rediculous card at first with high interest and monthly and yearly fees. Soon as my credit built up with some payments, yours isnt terrible, mine was in the 5's, I was able to get a better card. Dont spend much of your available credit. REALLY try and keep it lower than 30% and your uliliztion will look better and help your score rather quickly. im my case opening a new account with a higher ballance and transfering my debt to it (15 months 0% interest but was a 3% fee to do it) saved a lot of money over paying a couple of cards at 20-24% interest. If you have a good utilization % then you might even close the old account but if you are looking at a big purchase soon then it may be better to keep it open. Either way, my closing that horrible card actually made my score rise because of the newer better replacement card showing up. Again mine was in the 5's so it took a bit for new expanded credit acceptance but once it did it is currently going up very quick and am almost 700's. Id plan on a year though if you have negative stuff but you are ahead of me with your starting score already. 
For one thing, the new account could decrease the average age of accounts on your credit reports — a higher average age is generally better for your score. Additionally, if you applied for a private student loan, the application could lead to the lender reviewing your credit history. A record of this, known as a “hard inquiry” or “hard credit check,” remains on your report and may hurt your score a little.

The Discover it® Secured isn’t like most secured cards — it offers a cashback program and a simple transition to an unsecured card. Starting at eight months from account opening, Discover will conduct automatic monthly account reviews to see if your security deposit can be returned while you still use your card. Unlike most secured cards that lack rewards, this card offers 2% cash back at restaurants and gas stations on up to $1,000 in combined purchases each quarter. Plus, 1% cash back on all your other purchases. And, Discover will match ALL the cash back you’ve earned at the end of your first year, automatically. There’s no signing up. And no limit to how much is matched. This is a great added perk while you work on building credit.
Applying for and opening up a new credit card increases your overall credit limit compared to the amount you have used. This, too, can result in a nice credit score bump the following month, but only works if you have good credit. One drawback: You may initially receive a 10 to 25-point new credit score ding which will readjust after a few months of responsible credit behavior.
Many people, however, don’t have the time or don’t understand how to make their case, so they look into hiring a credit repair company to dispute errors on their behalf. These companies can charge a fee for their legwork (more on how that works in a minute), but there are times when the extra help can certainly be welcome. (Say you have multiple errors across credit reports or you’ve been the victim of widespread identity theft.)
Write a letter to the specific credit reporting agency that shows the falsehood, whether it is Experian, Equifax, or TransUnion. Explain the mistake and include a copy of the highlighted report along with your documentation. Although certain bureaus now let you submit disputes online, it’s not a bad idea to send this letter by certified mail, and keep a copy for yourself. The reporting agency has 30 days from the receipt of your letter to respond. The Federal Trade Commission provides advice on contacting the credit bureaus about discrepancies. Here are the contact numbers and web sites for the three credit bureaus:
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