Can I still browse my own store while maintenance mode is on?

No. While maintenance mode is on, every page of your store shows the maintenance screen to everyone, including you, even when you're signed in to the admin.

To check your changes:

• Briefly untick Enable maintenance mode (storefront shows the selected screen) in Settings → Web Settings → Maintenance Mode, click Save Changes, check the store, then turn it back on

If you only want to keep search engines away while you work, set Search Engine Visibility to No in General Settings instead. Your store stays open to people.