Why does the burndown chart go up at the start of my sprint?

This is because you've added backlog items to the sprint after you started the sprint. The starting point of the burndown chart shows how much work was in the sprint at the point in time when you started the sprint. So, if you hadn't added any backlog items, or very few, at that point, the burndown chart will start low. And if you add backlog items to the sprint after that, the burndown will go up, since the remaining amount of work increases.

So, you should normally pack the sprint first, and then start it when you are ready to start working. You can add or remove backlog items at any time, but anything you do after the sprint has started will affect the burndown chart.