If you've only had a secured card for a few months, and a secured card was your only option at the time, you probably aren't in a position where you can get a points card yet. Points cards with any value to the points and no annual fee require a decent credit score; you'll be limited to pretty poor choices if you get one now.
What I would do is wait until you start getting mailers for credit cards. Those tell you about what your credit score is, because there are a few kinds.
- "Build up your credit" ones - low balance, annual fee, total scams, mean you have around a 500 or so.
- Regular, basic cards, typically higher rates (15-21%) but no annual fee, often no points - means you're around 600 or so.
- Cards with some points, or cards with lower rates (11-14%) - mean you're closer to 650
- Cards with good point values (the 1%+ cards where you can get cash back) - typically starting in the 700s, or mid 600s with higher income levels.
- Excellent cards (Platinum type cards), sometimes with annual fees now in exchange for more points - 750+, with finer tiers particularly based on income.
Once you start getting offers for the tier you're interested in, likely you'll qualify for other cards on that tier. You also might be able to go one more tier up - but remember, if you apply and are declined, you'll probably have to wait six months or so until you apply again in order for that not to hurt you further.
One good strategy here if you don't initially qualify for a points card, by the way, is to apply for an entry level card (even with no points). I for example got a low limit Capital One (I know, I know) card back when my credit was poor. That turned into a points card, though, in a few years - because I built up a consistent history with them, that's often as valuable or more so than a credit score. As long as you qualify for the better card, they'll upgrade you to it - and likely without a hard check (at least in my experience).
Either way, I'd wait a bit. Probably a year or so. Things take time, and you don't want to rush when building credit - do it the right way and you'll do very well. Check your credit report frequently, join Mint.com or Creditkarma.com where you can get a free credit score so you know where you are, and then use pages that show you which cards are good/available at your credit score - like this one on creditkarma.com or this one on nerdwallet.com. Be aware those sites are usually compensated by the issuers, though they claim editorial neutrality.
