Great question, let me help you.
Dizziness is due to an inner ear condition, which may be related to an oral infection if the tooth is an upper tooth. The runny nose is unlikely due an oral infection, unless the infection is on an upper tooth as well. So, if you have an infected upper tooth, this could explain the runny nose and dizziness. You should get x-rays of these suspicious teeth and see if any infection exists. If it does, take antibiotics and have the teeth either root canaled again, or extracted. Sometimes the initial root canal will fail, and it may need to be done again. Keep in mind that the success of root canals go down when they are redone, so sometimes it is better to extract the tooth. This will for sure get rid of the infection. After this, you may see a significant improvement in your nose and ear conditions. If you have questions, please ask. Please click accept. Thanks