With Eddie dead, the current Earth Barry resides on was being erased from existence - as that timeline could have never occurred with Eobard being erased. Combine that with how executive producer Gabrielle said "he's from a different earth" and I come one of two conclusions; either A) the Well's we will see is from the other Barry's timeline (the one who saved his younger self), or he is the Reverse-Flash from another Earth. I'm going with my first theory though as Dr. Well's would still be alive in the original timeline where Barry first went back in time, only to save his younger self. This is because Eobard, after leaving his time, was stranded in the present - therefore creating a new Earth. So, the Well's from Eobard's original timeline still exists (as he pointed out when he says that 20 years from now Wells will build a particle accelator tcussions and so on - allowing him to make the best choice he can for any given situation on his Earth (which i am convinced is Earth 2 since we only saw one other Flash the night Barry's mother died).