Yes, OPK tests can be wrong and are wrong very often, especially for people who do not have textbook cycles.
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Yes, you can have EWCM and not ovulate, but if you are TTC, the best time to try is when you have EWCM. It keeps the sperm alive longer to help you to conceive.
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As to whether or not you should continue using OPK's every day, that is up to you, but if your body has not been cycling naturally, it could get quite expensive without helping.
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Do you know what is causing you to not have natural periods? When you ovulate, that is always followed by a period (if you are not pregnant), so if you are not having periods, that means you have not been ovulating. If you finally ovulated and had a period, that is a very good sign that things are getting better, but I would be surprised if you went straight from not ovulating at all to normal, textbook cycles. It could happen, but normally your cycles would get progressively better over time.
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It might be helpful for you to chart your temperature and CM (and anything else you want to chart). Assuming that you may be about to ovulate any time you have EWCM is a good way to go for TTC. If you notice a temperature rise around the same time as your EWCM dries up suddenly, you can pinpoint ovulation pretty well and establish a due date based on that information. This will be much more accurate than using your LMP if you do not have a textbook cycle when you get pregnant and prevent the need for early ultrasounds to date your pregnancy or pressure to induce if you conceived later than your care provider thinks. There's a lot of people here pretty adept at helping with charting and interpreting your chart, so holler if you ever need help.