@abc123def456
If you bought something online with a debit or credit card and did NOT log into your paypal account then of course it won't show on your paypal account as you bought as a 'guest buyer'.
However your seller may have processed that payment using their Paypal 'card reader' and so Paypal would show on your bank or card statement.
If that is not the case then contact customer services AND your card issuer to query the transactions.
Click on the words "Help / Contact" at the bottom of paypals pages and use the phone option in the blue band at the top OR very bottom of page dependent on what country you are in. Scroll down past the list of help questions and click on 'Call us' bottom of that page. Log in and get the code.
Freephone from a UK landline or UK mobile number.
OR
have you considered contacting Customer Service via Facebook or Twitter?
You can send them a personal message from their facebook or twitter pages.
It's: https://www.facebook.com/PayPalUK and @AskPayPal for Twitter.
Advice is voluntary.
Kudos / Solution appreciated.
