There are times that the browser is full of frequently accessed page resources. It may cause unusual behavior in the program. That's why you're unable to select the products or services when creating an invoice.
I'd first suggest signing in to your QuickBooks Online (QBO) account via an incognito window. It doesn't store data in the cache, so it's a great way to isolate browser-related issues. Here are the keyboard shortcuts:
Safari: Command + Shift + N
Mozilla Firefox or Microsoft Edge: CTRL + Shift + P