Sorry it's so long.

So my ex and I broke up due to the fact that he still had feelings for his ex. He thought he was over her but when he found out she was pregnant with another man, he broke down and realized he still had feelings and he was completely honest with me. He said he really liked me and he saw a future with me but he wanted to be over his ex first. I respect him for that! Although I really liked him, We hadn't said "I love you yet" so it was easier for me to to accept that. We still kept talking as friends after we broke up, he would always call and text me. I didn't call or text him because I was trying to give him his space. A few months after, we started seeing each other again and he said he wanted to take things slow, so we did. That started in May. Since then, we've done a lot together. He talks about his future and includes me in it and my daughters. He planned a mini trip for next month for just the both of us. I met his parents before but yesterday he wanted to take me back to them again. After his parents, we went to a lake about an hour away and he said next time we have to plan a weekend trip and get a cabin there. Note: We're not official yet. When we got there, he was looking for something and he asked me to look in his glove compartment so I do. Buried deep in there, I found a picture of his ex with 2 other girls (he wasnt in the picture). He said, I didn't know the picture was there. I just looked at him like okay sure. So he grabbed it and ripped it up. He got upset that I doubted him and was quiet it for a little while. After like 15 minutes, he hugged me, gave me a kiss and apologized. When he gets upset, I just need to give him his space and he'll get over it. On our way home, he mentioned something (irrelevant to this topic) and I corrected him. He said "okay girlfriend." I said "what?" And I meant like what? You're admitting I'm right?! But he said 'okay girlfriend" again and then said, you just wanted to hear it again and smiled. That caught me off guard and I didn't know what to say. Does that mean we're official again? 😅 and after the whole ex gf situation, am I doing the right thing by giving him another chance?