Being pushed away (long)

Jen • Mama to a beautiful baby girl. Henley Mae. 10.2.15
I've been married for 2 months, and with my husband for 3. We have a daughter who will be two months in December. I have always been faithful to him, and have never ever thought of cheating on him. 
Here's the deal..I recently reconnected with an old co worker. He is married and expecting his second child next year. We have talked about our families and so on. While I was up breastfeeding my daughter around 330-4am I noticed he messaged me earlier in the night so I responded. Apparently it was a huge deal to him. Yes we were previously fighting earlier that day because I didn't want to have sex with him, I'm always exhausted and when it was time for bed I wanted to sleep. (He comes home from work and falls asleep leaving me to care for the baby and his two together kids that aren't mine.) 
He brought it to my attention and I told
him that nothing was going on and we are just friends. Well he has been continuing to go one about this.
While I was at work one day he logged on to my facebook, I have it set up to alert me when this happens, and read my entire conversation with Alan. Then asked if I talked to him. I knew he snooped so I played like I didn't talk to him and he said the entire conversation word for word. Then blamed me for lying to him. Since this . I had to tell my friend that I can no longer message him because of my husband. 
He is pushing me away. He is constantly saying I'm lying and sneaking around. For some reason today my facebook wasn't working with Instagram. I've never had this issue before. So I had to change my facebook password. I told my husband about it and then ended up changing it again because it go locked out. He then accused me again of lying and sneaking around. I'm getting so sick of this. I've been in relationships before where they have accused me of things and it was that person doing it. They took it out on me to make them have less of a guilty conscious. I'm not lying to him nor am I sneaking around. He has access to all of my devices and can log on to whatever he wants. I'm just asking what should I do? Any advice? It's getting to be a strain on our relationship and myself. I'm home all day taking care of our daughter and at times his two boys.