The question should not be 'when to apply for a new credit card' but rather, when is my credit history and credit score sufficient to open a new line?
I'd first advise you to check your score with your institution (many have a free FICO Service) or on annualcreditreport.com
Please note, I'm referencing the federally mandated web site to retrieve the contents of your credit score for free, once annually, not another service.
Also, I would look to a credit union to open a new line of credit if you intend to carry a balance. A quick google search and I found 4 different credit unions with VISA/Mastercard lines with no fees and APRs under 12%!
Please note, most credit unions are by nature "Not for Profit" meaning they typically having lower interest rates and low/no fees.
Your credit score is a measure of how "safe" it is to lend money to you. Your limit is typically a reflection of how much VOLUME of money can be let to you at one time.
TL:DR - If your financial institution is starting to raise your limit, its a safe bet that your score is improving, if slightly. It typically takes 6 months - 1 year to build sufficient history to generate a meaningful score.
Also - this post may be of interest to you: For the purposes of building credit, does dividing up a loan help?