Is it permissible to wash clothes during the Omer?

Thank you for your question. It is absolutely permitted to wash cloths during the entire Omer period. Perhaps you are confusing the Omer days with the laws of the Three Weeks between the fast of the 17th of Tammuz and the 9th of Av. During those days the mourning period is stricter, and during some of those days (depending on different customs) laundry is prohibited. But, as I wrote, this is not the case during the Omer days. Blessings.