I think that telling your wife would be good for the situation. Although it may hurt her, it’s obvious that you’re trying to change your ways and I think she’d be able to appreciate that. Honesty is really the best policy, especially in a case like yours where your addiction seems to be affecting you greatly (at least greatly enough that you’re seeking our advice).
I don’t think that there’s a point in trying to keep it from her to spare her feelings. You’re taking steps to change your behaviour, and you say that your wife will forgive you. Imagine how she would feel if she were to find out in a way other than your telling her. I know that I’d very much prefer my partner to come clean about something than to find out in another way, and know that he thought he could “get away with it”.
I’m going to assume also that this is a paid service you’re using. If you’re spending a lot of money on it – and if that money belongs to both of you, and could be better used going toward expenses or a mortgage or whatever – I think she deserves to know.
Have you looked into any kind of counselling to help you get over your addiction? It might help. Also, it might help the two of you to get through this rough patch while you’re working on your own problems.
I also have to echo @blueiiznh‘s reply in that it’s not up to your wife to “keep you in check”. This addiction is yours, not hers. If you feel that telling her about it will help to give you the willpower to stop, then that’s great. But if you slip up and pick up the phone, it’s no one’s fault but your own.
Good on you for trying to get past this. I wish you the best.