6'2" 175lbs, Early 30's, married for 1yr, together for 4yrs, No kids. Lift heavy 3times a week.

My wife and I had a fight about 4 months ago due to our infrequent sex life. During the fight, she asked me "Will you still marry me if I had told you we won't have sex during the marriage" and I responded with a NO. She flipped my response and started crying that I married her for sex. She even made the same claim to a therapist during our visit and also threatened to tell our family and friends the same. This falsehood got me really infuriated.

We eventually had to sit down a few days later to resolve our issues(at least so I thought). But since then, she tries avoiding talking to me by any means possible.

For example,

Even though her company allows remote work, she still would prefer to go in every day and when she gets back in the evening, she only wants to talk for a few minutes, and then she goes into her room to be on her phone and TV. (Note: we sleep in different rooms because of my snoring)

During her off days, she would leave the house sometimes around 9-10 AM and not get back till about 5-6 PM claiming she was at Starbucks and also doing shopping.

Whenever we are going on a dinner date or event together, she would be so quiet in the car and would barely have conversations with me. However, once we get to the restaurant/event, she becomes lively, laughing and talking. Once we start heading back home, the cold attitude continues.

This behavior is really affecting me psychologically and I try not to let it show outwardly. Our sex life has gotten worst even after the therapy session and multiple discussions and I am losing patience.

I am beginning to suspect she might be cheating on me even though she does not appear like the kind of woman to do something like that. Sometimes, I am tempted to want to check her phone even though I know that's wrong.

How do you guys suggest I approach this issue?

Thanks in advance for your candid responses!