Can text messages be admissible if they are only one sided?

The admissibility of text messages is just like other evidence in the sense that it can challenged on the grounds of its lack of authenticity, relevancy or as being hearsay. However, without knowing the facts in the case or what the content of the message is it's not possible to fully answer your question.

As Mr. Orlando has noted, it depends...there are admissibility rules and a competent attorney will know whether or not there is an argument to keep them out as evidence.

Generally the content of text messages from a victim or other person than the defendant would be hearsay and not admissible in evidence. There are exceptions to the hearsay exclusion, but I would be impressed if a text message would fit any of the exclusions. However, if the mere fact that the victim transmitted a text message is called into issue in the case, then the message could be admissible in order to corroborate the victim's act of texting you, rather than to prove the meaning of the message itself. The victim, if alive, could also testify to having sent the message and what the message said, if relevant to the case.