Should I stop sharing my grief with her?

I've been talking to this girl and getting to know her a lot for over a month. We're not dating but she said she has some interest.

Recently I had a family member who took their own life, and it's weighing on me a lot. I didn't want to tell her about it, but it just spilled out when I saw her over the weekend. She has been very caring, supportive to me, and offered a listening ear. I appreciate it, however, I'm starting to think I should stop talking about it to her. Even though she's been very supportive, I can't help but think I'm burdening her. I'm going through a lot of sadness and grief right now, and I don't want to scare her away or lose her because honestly I'm afraid of sharing too much.

On the other hand, our dynamic is built on honesty and communication, and I don't WANT to stop talking to her during this time. I know she overthinks too, and I don't want to seem distant or that I've lost interest in her. I know it's alright to be a little selfish right now, but I don't want to hurt her feelings.

I don't know what to do.
Should I stop sharing my grief with her?
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