No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
I had at least that many (6) inqs. when I applied and got approved. But I was going for the Mastercard and didn't qualify so I got the store card. Were you going for the M/C also?
This is one of Citi's latest private label acquisitions. Citi is just not that very recon friendly and not a lot of folks have posted any success in doing so after the Capital One > Citi transition so, IMO, I doubt a recon is even possible given what the reasons for denial. You can try your luck again when your credit file is more optimal for approval and those inquires have aged.