Dating

Is this a trust issue and clingy behavior?

I've been dating a guy for 2 months. We text a lot and I don't mind because I'm fine with texting but things getting weird when he continuosly texting me everyday like never ending. Its like he can't leave me alone. He will stop only when he is super busy for a day or two. Then he text me again the same. He likes to questioning me a lot on how was my day, where have I been, who was with me, is there any other guy with me and other assumptions. The funny part is all his assumptions are not happening and not even exist. And I don't know how to explain to him because he refused to believe. He treat me with his trust issue but we haven't make it official yet. He said to me that I am a pretty lady so he can't fully trust me and doubt me everytime I said I had no other date other than him.
Is this a trust issue and clingy behavior?
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