The first thing we would ask in cases like this is what investigations you may have had already. There are a number of medical conditions like blocked tear ducts and the related dry eye syndrome which may be the cause of the swelling, and this can impact on the success for which one might hope. We answered a question on both a couple of years ago, and the answer is worth repeating for the wider context in which it places treatment.
Chinese medicine is based on an entirely different theoretical basis from conventional medicine, what is often called a different paradigm. The essence of Chinese medicine is a belief that the body, mind, emotions and spirit are all manifestations of an energy called 'qi' whose proper flow and balance means that everything functions the way it is supposed to. If this flow becomes blocked or disturbed in any way, then functional disturbances appear, often affecting all 'levels' of the system and for which needles are used by the practitioner to restore flow.
When someone reports blockages it makes one question immediately whether the energy of that area is flowing as well as it might, and a skilled and experienced practitioner could determine quite quickly whether, from the Chinese medicine perspective, there was something which might be done. Even if there were no immediately obvious signs in the area itself, the principles of Chinese medicine are founded on a notion of overall balance which means that symptoms are less critical, being indicators of a wider imbalance in the system rather than the necessary focus of attention. It would be worth your while to visit a BAcC practitioner local to you for an informal assessment of whether they believe that acupuncture treatment may be of benefit to you.
That said, we have to say that the research evidence for the treatment of both conditions with acupuncture is a little bit thin. There are a few studies, but one of the key factors in undertaking research from a conventional perspective is trying to reduce the variables, and this means being able to define clearly what the problem is. Blocked tear ducts have several possible causes, and this means that comparing like with like becomes more difficult, and the results less reliable. What research we have identified is of relatively poor quality, and if we were making recommendations based solely on that we would have to say that it would not be worth pursuing. However, our clinical experience is that where there are clear energetic blockages treatment can sometimes have a very direct effect, and it would certainly be worth seeking advice from a BAcC member local to you. There are, in fact, some quite useful studies of related problems like dry eye syndrome, and although it is rather technical this paperhttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC3355143/is both realistic and encouraging.This expert has to admit that it has not been the most successful area of his practice. While few patients have come specifically for this as a problem several have had it as a secondary problem, and even where the main problems have responded well this hasn't. That said, in the minority of cases where there has been a positive change the result has been welcomed with great joy.
Acupuncture treatment is always worth a try. There is very little chance of an adverse effect, and there are enough reports of treatment working for this problem to suggest that it is worth a go. The only issue for cases where there is less evidence is to make sure that a patient doesn't get tied into a long and potentially expensive course of treatment without any tangible benefit. In another context, Dr Johnson once described something as 'the triumph of hope over experience', and we always ask our members not to succumb to joining patients in a desperate hope for good outcomes. If there is nothing happening after four or five sessions it may well mean that nothing will happen.
If, however, the bags under the eyes are a result of loss of muscle tone, then we enter the area of facial or cosmetic acupuncture which has been in vogue for the last few years. There is no doubt that there is some basis for this work, as studies like this one https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3745857/suggest. There may also be reasons to do with straightforward blockage where treatment may have an effect. Our belief, though, is that treatment of local blockages really needs to be done in the context of a wider diagnosis of a person's balance, and only by doing this can the results be maintained.The last decade has seen a proliferation in people training to do 'facial acupuncture' or 'cosmetic acupuncture', many of whom have no background in acupuncture at all. We are not being protectionist in saying that in the courses which people do, many of which are of one or two day's duration, we do not think that anyone can learn properly skills which form a part of a three year training programme. If you do decide to seek the help of someone offering facial or cosmetic acupuncture we would fully recommend that you make sure it is someone who is also properly trained as a professional acupuncture practitioner.