In Singapore, psychiatric conditions are diagnosed using a face to face interview and an assessment of the mental condition (what doctors called mental state examination). Many of the doctors here use the DSM 5 diagnostic criteria. For patients thought to have anxiety or depression, the psychiatrist may also order a blood test to exclude abnormalities in the thyroid hormone level.
Given your problem of going to new places and fears of social situations, the first diagnosis that comes to my mind is that of social anxiety disorder (also called social phobia). Treatments would include psychological treatment (cognitive behavioural therapy) and medications (SSRIs).
It is interesting that you asked about anxiety and depression in the same breath. Yes, the two conditions or sets of symptoms are commonly reported by patients in our local setting and also in many parts of the world. Anxiety and depression oftentimes coexist in the same person and when you see one, you see the other as well. They are just like twins!
I hope you will get the help that you want soon. Wishing you speedy recovery.
