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No, you are not in any trouble for claiming your own child that lived with you for more than 6 months.   If you are qualified to claim the child as a dependent as per the above, you can do so.   If your ex also qualifies to claim the child, she can do so too, but the IRS is going to send you both letters and determine who needs to amend their return, remove the dependent and pay back any credits.   If you have already filed, she will have to file by mail and the IRS will work it out later, as only one of you will be allowed to claim the child.   There is no splitting of dependent credits.  

The general rule for qualifying children demands that the child live with you more than half the year and therefore children of divorced parents are usually dependents of the custodial parent.  "Custodial" parent definition under the IRS's rule (or for TAX purpose) is different from the court's definition.  For tax purposes, the custodial parent is usually the parent the child lives with the most nights.   

If you are both qualified to claim the child, the tiebreaker rules are as follows:

The child is generally treated as a qualifying child of:

• The parents if they file a joint return and claim the child a qualifying child;
• The parent if only one of the persons is the child's parent and the parent claims the child as a qualifying child;
• The parent with whom the child lived for the longer period of time during the tax year if two of the persons are the child's parents, they do not file a joint return together, and both parents claim the child.  
• The parent with the highest AGI if the child lived with each parent for the same amount of time during the tax year, they do not file a joint return together, and both parents claim the child;
• The person with the highest AGI if no parent can claim the child as a qualifying child; or
• The person with the highest AGI if a parent may claim the child as a qualifying child but no parent claims the child as a qualifying child, but only if that person has an AGI higher than any parent who may claim the child as a qualifying child.

What Happens When Both Parents Claim a Child on a Tax Return?