Avocado Tree Help

Chobella starts with ...
Hi, I grew this avocado tree from a seed and it is now 3 years old. It has been flourishing till we had extremely low temps and the heat was low. All the leaves fell off and I figured it was going through fall/winter. The branches started dying or turning into basically a dead stick, so I cut them back. They continued to die and keep ruing the healthy branch. Leaves are coming back and new growth is starting, but one of them is killing the new growth and its spreading. Please help me save my tree. It is a strictly indoors tree and u just love the way it looks.
I have not fertilized it, except for some sugar water in the beginning. I did not want to touch it till inreveived feedback. Thank you.

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