Will it be difficult for me to refinance my car loan?

I applied yesterday for a new apartment, so obviously my credit will be checked, among other things. My mom co-signed for a new car for me about a year ago and I am now plan to refinance my car loan in just my name. Am I going to have a difficult time getting the loan being that I just had my credit checked for a new place? I have about 2.5 years credit history with a fairly average credit score.

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