The out-of-state convictions will get reported to the National Driver Register and NY will find out about them. Those out-of-state convictions will count in NY as though they had occurred in NY. In NY, 3 DWI convictions in a 25 year lookback period can result in a permanent license revocation. You really need to see an attorney to find out where you stand and what is likely to happen to your license.
I suggest you also need to stop driving after you have had anything to drink. Alcohol impairs your ability to drive safely; your reflexes, perception and judgement are all affected. People drinking alcohol do not notice the impairment because the alcohol relaxes them and makes them feel good and thus capable of doing more than they really are. This leads to accidents. Moreover, each time you get caught driving DUI the penalties will keep getting worse. You are now at a point where you risk being sent to prison if you get more convictions for this offense. If you are having trouble avoiding alcohol when you’re going to have to drive later then that suggests an alchohol addiction that needs to be dealt with. Few people that have alcohol addictions are willing to admit the addiction until something really serious happens because of the drinking that forces them to face the problem. Let your 3 convictions be a wake up call to you that you may need help. Don't wait until you've caused an accident and seriously injured or killed someone to get that wake up call.