Am I having an extra marital affair? And if I am what should I do now?

I am a 42 year old woman, married for 14 years, to the love of my life. We love each other from our college days. Let us call my husband X. We have two young daughters. I particularly have no problem with my husband. I do a lot of work at home, especially with the two kids around, plus I work as well, with X and we run our own business. At home, I get stressed with all the work and the kids and I feel I get no help from X there. I have some health issues as well. I also feel X has no time or interest in listening to my personal problems or emphasizing.

About a year back, I reconnected with an old friend from college (where I and my husband also studied). Let us call this friend Y. He too is married with two kids. Once I had mentioned to X that Y had made friendly advances to me in college but nothing beyond that had happened. Now there was a project that I and X were working together on, where I felt that Y could help. So I asked if he would mind if we worked with Y on this project, as he could probably contribute. X said we should work with Y if he can contribute. So Y helped with the project and the project got over. During the duration of the project I ended up discussing other things with Y, like gossiping about some of our common friends, other personal issues like my health, his money problems, and others. Soon, we were exchanging multiple messages during the day, and at times I would be making 4-5 calls a day to him. These calls and messages were without much agenda, we would generally chit chat, and I realized this made me feel good. It was a stress reliever. Y would listen to my problems and I thought I had someone who would at least listen to me. There was no sex involved, but it was just that I felt good chatting or talking to him. Along the way, I felt that if X found out about the frequency of the messages and calls, he will get upset; and so I began deleting all traces of messages from my phone.

One day recently, my husband caught me deleting a picture of him from my phone, by accident. I blurted out that I was deleting that picture as it would have upset him if he saw it on my phone; I anyway had no intent of keeping the picture which Y had sent me. And then he grew suspicious. So he checked my phone. He saw evidence of text conversations with Y which were deleted. He also saw that some messages were not deleted and yet I had the highest number of messages with him. He also saw that I was making multiple calls to him during the day.

X knows that I have been working on Phase 2 of the project with Y. However I did confess that all these calls and messages were not on account of work.

Now I have tried my best to explain to X that it is not what he thinks it is. But I am unable to convince him. He says he is very very hurt about the fact that I cheated on him. He feels cheated because I was deleting the evidence as I felt that it would upset him. He asks me that if I knew it would upset him, why was I continuing with it? He is disturbed and says that he has lost me, as I have found someone else to share my personal things with; that to him is a bigger loss than mindless sex with a stranger.

Now I am at a loss. I definitely do not want to destroy my family or break off with my husband whom I love; nor does Y want to do that with his family. Am I having an extra marital affair? Have I really cheated on my husband? What should I do now?