Can we go back to normal friends after sleeping together?

Anonymous
Long story short, my best girl friend and I slept together over the summer. It was a bad decision because I knew she had feelings for me, but she told me that she could handle a friends with benefits situation. I moved away a few weeks after that, and she got clingy. Nothing strange, just texting me all the time. But, I attributed it to her missing me and seeing how her best friend just moved away. She came to visit, and we had sex again. She also found out I had made out with another girl, and just by her reaction I could tell she was jealous. After she left, I confronted her and asked her whether or not she ever got over me, because it seems like she didn't and was holding on to the idea that we could be together eventually. She freaked out, texting me a bunch saying that she didn't have feelings for me anymore. Since then, I've tried to lay low in the friendship a bit, and treat her like a normal friend. The only problem is she's become a bit clingy. It's not too bad, she'll text me every 3-4 days talking about her life and what we'll do over breaks. She sent me a mid terms care package a few weeks ago. (She's a big gift giver, and sending people shit) But she throws in the occasional "miss you" text, and I don't know how to read it. Can our friendship go back to normal? I think she's trying to make it that way, but I also don't know if she still has the feelings.
Updates:
+1 y
we used to text everyday, and she would send another text if I didn't reply. She stopped doing that, and only texts me now every few days. When I confronted her, I reassured her that she's my best friend and that I care about her. So I don't seem like a total asshole here.
Can we go back to normal friends after sleeping together?
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