I had a vocal cord nodule removed, but it did not cure my hoarseness - what can I do?

Another opinion. If your nodule is gone and you are still hoarse and you have discussed this with your ENT and have not gotten help then you need another opinion. Find an ENT who has a special interest in the voice. You should have a videolaryngoscopy with stroboscopy and a consultation with a speech therapist.
Follow up. You should contact your surgeon for a re-check and re-examination of your vocal cords. This can usually be done easily in the office.