I agree with what others have said
Your doctor is wrong and doesn't know what he's talking about if he is replacing a cyclical HRT with a no bleed one, unless he thinks you are post-menopausal. Had you been more than 12 months without a natural period before starting on HRT? If this is the case then you could try a no-bleed type. If you were still having irregular periods and less than 12 months since last natural one, then the usual advice is to try a continuous no-bleed type at age 54 when most women have become post-menopausal.
Even taking this into account the most important reason for not trying the Premique is that you are changing both the oestrogen and the progestogen from that in the Elleste Duet, so if you are allergic to one of these formulations you won't know which one, whereas on a cyclical HRT you could see if you react differently in the different parts of the cycle.
Again in view of the fact you had a reaction to something in Elleste I woudn't go for any of the Prem types - because of the horse oestrogens most of which are not found in our body.
If you are going for a tablet HRT then the best option is Femoston as we have advised, unless you take separate oestrogen and progesterone.
Personally I would not take it but I appreciate your difficult dilemma having to argue with your doctor, who really shouldn't give you a product you do not want either!
Good luck
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Hurdity x