The answer to your question is no, if no reason is given, then a judge will not grant a protective order (what a restraining order is known as in the State of Texas). Keep in mind that even if you think that is no reason for a protective order, the person asking for it may disagree or may make untrue allegations in order to get the judge to grant one.
However, in order for her to qualify for a Protective Order, she must be able to show that you have are a relative or were involved in a dating relationship or that you lived together. She must allege that you committed family or dating violence against her or a member of her family. That doesn't sound like that is the case here. My advice to you is to evaluate the relationship you have this person. If it has gotten to the point where she is threatening you with this action, maybe it is time to let it go. If you still want to be around the baby while the ex has custody, there's really nothing she can do to prevent it (under the facts you've to described) but you may push her to file for a Protective Order and make some false allegations. Even if you didn't do anything wrong, this will put you on the defensive and would probably be a situation best avoided. Perhaps you should back off.
I'd suggest talking to a local criminal defense attorney who handles protective orders if you have more questions.
Disclaimer: This answer is provided as a public service and as a general response to a general question, it is not meant, and should not be relied upon as specific legal advice, nor does it create an attorney-client relationship.