i can see the whole branch.. but i cant really see a leaf to make any diagnosis ... nor the trunk at ground level

the easy way.. would be to cut it down to 3 to 6 inches ...

but if there is a bug.. though you are getting rid of the majority of them ... you would just have to wait and see if you got rid of them all ...

that said.. it would be weird to have an infestation of one part .. bugs arent really that selective on location ... i suspect injury to that branch/trunk ...

ken

Trima,
Go outside with a pointed shovel and dig a little around the roots about a foot or two around the branch that is browning.
See how moist the soil is, and if there is anything in the soil that doesn't look right.
How close is that climbing rose anyway?
See if the roses roots are sneaking over to your wax mytle tree in that area.
you wo't hurt the plants by digging a little bit, jsut not too deep.
i have a feeling something is going on with the rose and the mytle and the watering situation.
have you fertilized the rose bush this fall?
Wax myrtles really don't like a lot of nitrgen at all, they burn easy.
Just a thought.

i doubt any rose .. is going to out compete an established shrub ... [except for a the very few.. old time monster roses ..]

there is probably some 60 foot maple 5 feet just the other side of the pic.. lol .. and even still i dont see that it would affect one branch ...

ken

Trima, you may not be aware that wax myrtles are pretty susceptible to a number of fungal disorders, especially in Texas. Some are soil borne while others find entry into the plant body via injuries such as pruning cuts. The type of die-back you've shown us is absolutely typical.

I strongly suggest that you make a call or visit to your local Extension office. Staff members should be able to walk you through some steps that may help you self diagnose the problem. I would do that BEFORE you go digging or cutting.

My wax myrtles are doing the same thing. I'm in Georgia and we just had a cold snap. The leaves look as if they browning from the tips down. As if they have been burned. The whole branch is affected. And idea why this is. They are 3 feet tall.