Appropriate statistical analysis for 2 groups with 3 possible outcomes

Hi all,
I’m a little stuck regarding the most appropriate test to use to determine statistical significance. I have the following scenario:

- Two groups (treatment group and control group)
- 3 outcomes (improved health, worsened health, no change in health).

I figured I can’t use t test since it isn’t continuous data. Also tried chi-squared, but that only tells me if there’s a difference between groups; it doesn’t show whether one is better than the other (for example a mix of “improved health” counts, “worse health” counts, and “same” counts in either or both groups can lead to a large chi-squared value showing a difference between treatment groups, but that doesn’t mean one is better than the other.

Thanks in advance for your thoughts!