Your purchase history can be found by tapping the menu ☰ icon and selecting Purchases.
Purchase history is separate from the your Venmo feed. By default, purchases are only visible to you, and only shared if you choose to do so on a per-purchase basis.
Additionally, you can always view your Venmo statement by visiting venmo.com on the web, then navigating to Settings > Banks and Cards > scroll down to Transaction History (or visit this link on the web directly: https://venmo.com/account/settings/balance/statement). This information can be viewed on the site or can be downloaded as a CSV by clicking on the “Download CSV” button next to the view button.