Since your intent was to move back to Ohio, your time in Delaware was only a temporary absence. You were a full year Ohio resident.
You must file a DE non resident return and pay tax on the income your earned there during the 3 months. You file a full year resident OH return and report ALL income, including the income earned in DE. OH will give you a credit, or partial credit for the income tax paid to DE.
If you are self employed, there will probably be no credit from OH. OH has a 100% Business Income Deduction (BID) (with limits), so there is no double taxation. Effectively, working out of state for 3 months results in state tax that the self employed would normally not have had to pay.