For recently diagnosed severe anxiety disorder is it better to have just 10 sessions with a psychologist or go weekly for 12-18 months?

Ten sessions is: not a long time to make progress w/anxiety disorder but some progress can be made. Every case is different. You can start w/ten sessions and see where you are. After a few months sessions may taper to 2-3 weeks apart. What the person does between sessions (eg, practice) is vital to progress. You can do it. Peace and good health.

Something in the mid: 10 sessions is likely not going to be sufficient if your anxiety is severe, but that does not mean you will necessarily need over a year of therapy either. You should come up with some specific goals and continue with therapy as long as it takes for you to achieve those goals.