Will my warrants show up in a new state?

I just moved from Texas to Ohio, and I need to go down to the DMV to get my Ohio D.L/I.D card. Now from what I hear, the DMV will run your name to check for warrants. I have several unpaid tickets in Texas that may have turned into warrants. Will I be arrested? Will I be able to get my D.L?
They are all misdemeanor citations/traffic tickets. But I have quite a few, and like I said they may have turned into warrants by now. I just need my I.D. Even if they do not arrest me, will they still issue me my Ohio I.D/DL?
 
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