Got a Pre-Approved, but have a question..

[MagicmanAA]

So a couple of weeks ago I applied for a FHA loan and my credit score was EX 625, Trans 713, EQ: 661. Just last week, my scored jumped up because my first credit card finally started reporting. I subscribe to Score Watch, so my score is now EQ: 690, Trans: 729, I am sure my EX went up too, but I don't know to what. So now, I just got the Pre-Approval letter from the lender I am working with. ( I am excited) Can I ask them to check my credit report again so I can get a better rate or do the lenders already do this before I close on a house?

Also, if I got a pre-approval from a lender , am I stuck with that lender or can I try to get another pre-approval from another lender?

[mauve]

They won't lock in your rate until you're under contract - I'm not sure if they'll pull again before that. 

Also, you can absolutely look for another lender.