Is Xanax and Lamictal a good combination for terrible anxiety and bipolar depression?

Hi, Binx! Many Bipolar patients have associated anxiety disorders so this might be a good combination for you. The Lamictal is a mood stabilizer that helps with depression and to a lesser degree anxiety. Xanax is a benzodiazepine and only recommended for short term use as it can be highly habituating and cause increased anxiety, depression, sleep disturbances, etc. when used long term, but it is an excellent choice for panic attacks.
If the Lamictal works well you might eventually want to consider a safer option for your anxiety symptoms like buspirone. You might even find that you no longer need an anxiolytic. There are also medications available like Latuda and Vraylar that are specifically prescribed for Bipolar depression along with a mood stabilizer.
There's no reason to be afraid of taking them (that's your anxiety talking). You might initial feel some dizziness and/or drowsiness but that passes after several days. Perhaps start the Lamictal on the weekend or when you have a couple of free days to see how well you tolerate the combination.
Best regards and I hope you're feeling better quickly.