Messages in your 'my ebay' are NOT slowing your computer down. If those messages are also going to your email and you can simply delete (also need to delete items in trash, basically have to delete twice to open up space on a hard drive. You can also delete messages on your 'my ebay' under messages.
Both eBay and Email are websites; those websites are holding your messages; not your computer (hard drive)
If you have a slowing computer- go to history and empty all previous history, cookies, downloads etc. This will require you (if you delete cookies) to re-sign in on all websites that have name/password including causing banks etc. to email/text you since they 'don't recognize this computer' (for the first time)
