If you have the Tree Climbers Companion ( Which you should buy anyway!) on page 25 tells you how to "Isolate" the line by using a second throwbag a small( non rated) carabiner and a stick. Very simple technique. Very parctical and when you get good at very easy to implement.
Sometimes if the branch is strong enough to support your weight you can actually climb it as it is and fix it when to reach the TIP. All types of ways to deal with it it just takes practice, frustration, determination to continue building your confidence.
By the way welcome to tree climbing!