Boyfriend in love with his ex-girlfriend?

Hello community!

My boyfriend and I are a fresh couple of 3 weeks. (17 & 18)
Before he met me, he loved this one girl a lot, and they wanted to be together. This girl had a boyfriend at the time, which she broke up with for my boyfriend, but when he asked her to be in a relationship, she declined.

He was very depressed and had a hard time forgetting her. Then he met me, and we hit it off really well.

Sometimes he mentions her, but I thought, they cut things off for good, and I wouldn't have to worry,
if he's still in love with her.

Today thought, he told me, he's meeting up with her, to go to the hospital together.
(Both have to do some check up's, so they had the brilliant idea, to do them together. I'm not sure,
why he hadn't asked me to accompany him.)

I was a little insecure by them, because he hadn't told me, that they still are in contact.
I asked him, if he got a crush on her, and he answered with: "Yes, I have feelings for her, but I know, that a relationship with her would be bad for me."

I wasn't so sure, what to say, so I said, that I don't want to be hurt.
He told me, he wouldn't hurt me.

He was sitting on the bed, and I was behind him, and I saw, that this girl canceled the hospital trip, and as he was scrolling through their messages, I saw how that they text hearts and kisses back and forth.

I'm kind of hurt, and very insecure. I'm afraid of him loving this girl. I couldn't live with that.
My question is, do you think, with your objective perspective, that my reason to be insecure is reasonable?

Sidenote: He is kinda friends with another ex too.
Boyfriend in love with his ex-girlfriend?
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