Writing Stack Exchange is a question and answer site for the craft of professional writing, including fiction, non-fiction, technical, scholarly, and commercial writing. It only takes a minute to sign up.
“Ruby was thinking hard, too hard for her own sake. She wanted to talk with him but it seemed like she wasn't able to. She wanted to caress his hand, to show him how much she cared about him. She was desperate for something so banal, she thought how absurd was the situation I can touch him right? I mean we're a couple, we're in a romantic relationship...so...why, even when I touch him, I feel like I'm doing something wrong? However, she hadn't/wasn’t let/letting her emotions show on her face.”
Slighly different tenses, the one that fits in the paragraph is "wasn't". "Hadn't let" could infer that she wasn't letting her emotions show before, but what abour now? "Wasn't letting" infers that she was and still is hiding her emotions.
Personally, I would opt for a positive verb rather than the contraction of not.
Going on just the two options (and not doing away with contractions entirely like echo3 suggested), It depends entirely on the tense you are trying to write in. For example, "Hadn't let" assumes that beforehand Ruby was not letting her emotions show, but it doesn't give anything concrete in terms of presently. Conversely, "Wasn't letting" directly tells us that right now she was not letting her emotions show, but it doesn't tell us about whether or not she had shown her emotions in the past.
tl;dr It depends on whether you are referring to the past or the present.