No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
I'm in the same situation. I have a IRS payment plan from 2005, but didn't disclose to my lender (Wells Fargo) because they only requested the past 3 years. I'm concerned because I don't know if the transcripts or IRS will inform them that I'm on a payment plan for owed taxes in 2005. I'm officially in escrow so I don't know what to expect. My application came back with an instant approval.
One more thing, even though your application came back with an "instant approval" you still have to go through the entire underwriting process. Disclose the installment debt to your LO today.