I don't have depression/anxiety outside of pregnancy, but suffer terrible anxiety when pregnant so completely understand. I literally did about twenty pregnancy tests each time. I can definitely recommend an early scan, I have had two each pregnancy (one an NHS because of a bleed but the rest private) and it is reassuring to see that things are progressing at least. Where i went it was only £40 and was money well spent.
My other advice is to stay away from google, it is not your friend. The people on the internet, although lovely, are not a representative sample of pregnant people. Remember that people with happy, healthy pregnancies with a good outcome do not usually need to post on the internet, so you will see many more people who have sadly not had good outcomes.
Finally, take it one day at a time. Say to yourself, "I am pregnant today" and celebrate that, but don't focus too much on whether you will be pregnant tomorrow or next week or next month, it's too hard.
I have had 'easy' pregnancies from a physical point of view, but pregnancy messes with my mind, and if you already have depression and OCD then definitely raise this with your midwife as they can get you support. Congratulations and best of luck.