Appeared clingy at the beggining. How do I fix it?

Hello. So I met this girl on dating site. We kicked off fine and immediately found each other on good terms. We flirted, chatted etc. After some time - we met. After we met 3 times (she is really shy and I like that in her) she told me she wants to take things slow and see where it gets. I told her I like her, but I'm not going to pressure her and see where it goes. Then we met again. We already broke touching barrier after first date, I can see she likes me. One thing tho: I came on way too strong. I recently started to be clingy, overthinking. I can see she does not like
it, but she haven't said anything regarding that. She is still texting first in the evening or when she is with friends, but her
replies are shorter, less engaging and she is barely reacting to flirting.
I think it's because I was too clingy, texting a lot, replying instantly.
Bottm line is, we agreed to take things slow after third date. She likes me, but I can see she is starting to doubt me because how clingy i behaved.
My question is: how can I change her mind?
I want to change and I really don't want to put her in uncomfortable situation.
Appeared clingy at the beggining. How do I fix it?
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