I currently have a Gmail account with a really long email address. I want to change the primary email to a more professional one. Is that at all possible? And what do I do about all of the Google apps that I use? Will I have to start a new photo cloud and a new Google Wallet?
A couple of people have pointed out a similar question here. The accepted answer was to create a new account and forward your old emails to the new account. That would not move the other apps that you're using. You would need to either move the contents of each app to the new account, or switch back to the old account to use those apps.
If the only thing you want to change is your email address, you can keep using the same old Google account and add the new address as an alias. There are two steps to this:
Create the new account and forward all email to the old address. In the new account, click the settings button (gear icon in top-right) and go to the "Forwarding and POP/IMAP" settings. Click "Add a forwarding address" and add your old email address. Afterwards, choose the "Forward a copy of incoming mail to" and select your old address.
Go back to the old account. Click the settings button and go to the "Accounts and Import" tab. In the "Send mail as" section, click "Add another email address you own". Enter your new email address.
You can then continue using your old email account. If you receive any emails at your new address, they will appear in your inbox. If you reply to them, Gmail should automatically respond from your new address - theoretically nobody would know about your old address.