Old timer first time posting on one of your threads, I think. I give facts from my own personal experience, and my years here.
I am more than a dozen years out. I was able to R w/ my H, and am pro R if it's the right circumstances.
1. It is NEVER a good idea to share a therapist for IC. It's NEVER a good idea to go to CC with a therapist either of you use. It is impossible for them to maintain an indifference and not side w/ one or the other.
2. Your counselor is dangerous. She is not just lousy she is telling you and forcing you to make decisions based on your partners level of readiness. As someone that has worked w/ people to work on health understanding readiness is huge in creating effective lasting change.
3. It is not your burden to bear his shame. Him not wanting to tell others is based in shame. You have every right to share what you are going through. His actions have created terrible trauma for you. He is clueless that he has traumatized you, and isn't owning the fact that he has. Or is refusing to accept that he did this damage.
4. The fact that he deleted shit off your phone should be a non-starter. I know you are scared, and don't want your relationship to end, but here is a cold hard fact. It has. Your relationship as you believed it to be, never was, and what was died as soon as he cheated, and you knew he cheated.
Here's where shit goes sideways though. That doesn't mean that it wasn't good, or that the love you had wasn't real. It was broken, very broken, but not because of any short coming you had.
I understand that you are in pain, and you will be for a good bit no matter what path you choose, you have been hurt and traumatized. I urge you to step back and slow down. You cannot rush this, and the only way to heal, and heal right is to go through it. There are no shortcuts. There are no easy ways. The best thing you can do to simplify it and allow you to heal properly is to make you the #1 priority.
Get yourself a counselor that specializes in trauma, deals with things like rape, murder, grief trauma, NOT infidelity. Infidelity is his problem, not yours.
Sit down and figure out why you want to stay with this man. If fear of the unknown, being alone, and finances are included in those reasons then you need to step back and figure out how to fix those fears first. Staying because you are afraid usually does not end well.
Then figure out what your absolutes are. What do you absolutely need from him.
Honesty, transparency, going to IC, allowing you to discuss what he has done to you, Your absolutes may be different from mine. That's ok. But you have to know what would need to happen for you to walk away. Once you figure those out you tell him. DO NOT share w/ him until you are ready to walk away.
I know you aren't married, but may have been together long enough to comingle expenses, own things together. You need to see an attorney so you understand how separating will effect you financially. What you need to do to be able to financially be able to walk away.
The reason I emphasize this is again not staying in a relationship where fear makes you stay. You want to stay because you feel loved honored and respected, and if you don't you feel strong enough to say so, and see action to make you feel those things.
Keep reading and posting.