Got a cashiers check from a lady named Christina Phillips and sent extra on the check saying to money gram the extra money to her shipper to pick up the wedding dress she wanted to purchase from me. I need to know if she's a scam

Just about count on it. Anytime they ask for you to money gram or use a green dot card and send you excess money to send back, run, do not walk, away!  By the time it actually bounces better then a super ball in a concrete building, you'll be holding the bag and owe it all back.  

Sending fake checks through the mail is a crime so contact the US Postal Service Inspectors:  
https://postalinspectors.uspis.gov/forms/MailFraudComplaint.aspx
https://www.usps.com/
Or take it to your local postmaster!

You can also turn it over to the FBI as well. Along with any emails they may have sent you. IC3 is the cyber crimes division of the FBI.

http://www.ic3.gov/default.aspx
http://www.fbi.gov/

Curtesy of:
http://www.consumerfraudreporting.org/checkcashingscams.php
http://www.bankingquestions.com/

If you receive an email or letter in the post / regular mail saying you won a lottery and they send you a check? Or you sold something on Ebay and the buyer paid with a check? Or  you took out a loan from a distant or online bank and they sent you a check? You can just take the check to your bank and cash it right?

WRONG!  And what is worse, if you cash it, in most states in the US, you may be guilty of passing a counterfeit check, money laundering or worse. Clark Howard did a piece on his radio show about a man in California who was arrested for cashing a bogus check. In other words, by merely attempting to cash the check, you could go to federal prison!