Woke up with deep burning in left temple. no pain or other headache, but earlier the ear on same side was ringing. should i go to er?

May be not: First burning feeling in temple without pain is very non specific. If you had ringing in ears, without any pain, ear discharge it is less likely emergent scenario. However, if you have burning in the temple with blurred vision and throbbing headache it can be serious. It would be good to see your primary physician or going to urgent care than emergency department