I personally would leave it open for 6 months to establish positive credit history.
Did you check Discover’s pre-qual for the student card?
I’d leave it open and show usage with low utility.
OP, which brand student card did you apply for?
Which brand of secured card did you get?
Banks will often try to help in this way, trying to provide some reduced credit card if there are reasons they do not grant the card applied for. I was rejected for a regular PenFed CC in 2014 due to high utilization on other cards, and zero history with PenFed. They allowed me to use the same HP to open a secured card for $500. I used that for just over a year, then applied for the PenFed Promise and closed the secured card after that.
However, depending on which bank this is, I would suggest calling their customer service line, or asking to see the branch manager. No teller should be encouraging you to apply for two student credit cards at the same time. This bad advice needs to be noted to either the phone support or the branch manager, because the most likely situation is the teller is trying to go for some bonus for getting customers to apply for cards.
Because you got bad advice, raising this issue to management makes them aware, and you should ask to be reconsidered for the student credit card. You should ask nicely, but firmly and persistently.
Let us know how it goes. Good luck!
Op has the BOA secured cc, which imo is one of the better ones.
There are some other details which may have played a factor on the credit decision. I’ll allow op to share if they choose too.
The good thing @mineiro, since it was BOA, more than likely you will only receive one HP showing on your credit report. Although you didn’t get the card you applied for, you were approved for a card.
1 HP = 1 card balances out.