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There are special provisions regarding drugs considered controlled substances, but for those that are not, the US Embassy Seoul advise:
For medications that do not contain narcotics or amphetamines, up to six bottles of medication (or equivalent to a three-month supply) will be permitted into Korea, provided they are for personal use only. Visitors must bring the original prescriptions, a letter from your doctor specifying the medical condition, and a statement from your doctor on the medicines you are importing.
What I would expect is that you will have (had) no problem. However this is based on a couple of very unsatisfactory assumptions: (i) were problems to be expected we would have heard something of cases where issues had arisen and (ii) however arbitrary bureaucrats can be at times, there is nothing to be gained by depriving you of these medicines.
Forging a doctor's letter should not have been required as the odds of being asked for one would seem miniscule. However, even someone being particularly officious may care only that you have a piece of paper and next to nothing for what is written on it. I have no experience of South Korea but I have never, ever, anywhere had any interest whatsoever shown in my medicines - not even to determine they happened not to be prescription ones. In fact at the moment I can't recall ever having my bags searched on entry to any foreign country (maybe US and Australian Agriculture each had a quick look?) and that would be a step before examining the labels on bottles and tubes.
It is too late to abide by the regulations. You choices seem to have been either to leave them behind and replace them in Korea as required, or to take them with you and hope for the best. Either (as I would expect) no uncomfortable questions and I hope a nice time in Seoul, or, what seems the worst plausible possibility, your medicines are confiscated but you are still allowed entry. So even the 'downside' is probably only the need to replace them once in Korea.
Of course, you could decide to postpone your trip until after consulting your doctor, but that really does not seem to me necessary.