I can't legitimately give advice on whether or not you should tell your kallah* about your addiction, because when I was in that situation, I didn't. I could only share my own experiences.
skeptical
This whole issue started when I was a young teenager. With the internet in its infancy, I had my own computer in my own room and I had hours to explore. I knew that what I was doing was wrong, but I was extremely curious, nervous about the topic, and fascinated. I tried a bunch of times to install filters, but then I would always open them up. I tried to write tiny letters on my calendar to indicate that I would try to stay clean those days, it didn't work. I deleted accounts to certain services but would then just open new ones. I was just way too interested in the stuff.
I got a little older and went away to a yeshiva. While at yeshiva, I was able to stay clean without a problem. I didn't keep track how long I was clean - that wasn't really a thought at the time, so I have no idea how long each stretch was. Each time, I thought I had it beat. Then I would go home and just out of curiosity, I would go to certain programs/sites just to see if the people I use to interact with were still there. Pure stupidity. In reality, I was testing myself to see if I still had the desire for the stuff - and I failed miserably. And you know how it usually goes. Once I fell, I was a failure and would stay down for a while.
Then I started going out, looking for a shidduch. Would I share this most embarrassing side of me with anyone? No way! Once I'd get married, there'd be no reason to do this stuff anyway, I'd have the real thing and then I'd be cured! From the time I met my wife until about 3 months after my chasuna, I was clean. I remember just before my wedding, I was a bit down that I had never really beaten my YH before it was game over for him by default. How foolish! Life after marriage is stressful too (who knew?) and one day while at home on the computer, I once again decided to check out places I used to frequent just to make sure the YH was really dead. It wasn't.
A year or two after I got married, while I was at work, my wife came across a browser I had accidentally left open. That was the beginning of years of pain and anguish for the both of us. She was extremely hurt by my actions, and my world was coming crashing down around me. My deepest, darkest secret was out. I may have resolved to stop, but at that point it was only half-hearted. The truth is, I didn't see why she was so bothered, and I didn't feel she really had the right to be. This stuff numbs us, it numbs our feelings, and it did a good job on me. To me, it was just simply a way to wind down at the end of the day and though I knew it was wrong, I felt it was something that was between me and Hashem. My wife on the other hand wouldn't buy that. She started speaking to people in the community and soon Operation-Get-Me-Into-Therapy-Or-The-12-Steps began. I was hurt, frustrated, embarrassed and annoyed. My deepest darkest secret, the one I wouldn't dare breathe to a soul was coming out...
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Rabbi Dr. Twerski
There is an adage, "You're only as sick as your secrets." Revealing information that may ruin a shidduch is understandably very difficult, but keeping it secret creates a constant anxiety and a barrier to mutual trust and sincere communication. Marriages have enough problems without adding secrets.
In the case of alcohol or drug addiction, we generally tell people to avoid even getting into a relationship before one year of solid recovery and with the approval of one's sponsor. One month sobriety is hardly a beginning.
There are many variables. How long was the addiction? Does the person still have urges?
Whenever one decides to tell, one should say, "I must tell you something about myself, but it is with "Bal Tomar." You must promise not to tell it to anyone else.
Twerski