So basically in FIFA 14, my pro in career mode is too valuable to be sold to other teams because my value is super high and team transfer budgets are too low. I don't want to be stuck in La Liga. I'm at Barcalona but the only team that seems to have enough money to spend is Real Madrid, is there a way to increase transfer budgets on other teams to be able to buy me or is my player stuck?
There is no way to increase other teams budget. You should try to get your player away from the club.
You should have thought this through. Though you can just wait till your contract has expired so people can get you for free. You can also ask your club if you can go out on a loan in the meanwhile or just ask them to put you on the transferlist so they sell you for probably less than they want to sell you. Though as a pro in career mode you should just sign short contracts if you're good enough to go to other clubs. Don't sign a 5 year contract.