Good morning. If all you sent her were texts and these texts were confined to a short period of time, then the girlfriend is pretty much threatening only to make you stop because that is not going to amount to enough to substantiate an harassment criminal charge. But, if it continues, it not only could be enough for an harassment charge but also cyberstalking...which has now been codified as a crime to deal with texts, emails, etc. You need not worry at this time as long as this was an isolated event, but you will need to discontinue any further communication with this girl. Next time you have the urge, write it on paper and then throw it away....sending a text or an email causes it to live forever.
I hope this has given you the guidance you were seeking. I wish you the best of luck!
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The information given here is not legal advice. As all states have different intricacies in their laws, the information given is general only. This communication does not establish an attorney-client relationship with you. I hope this answer has been helpful to you.