There are many things that could be going on to cause the aggravation beyond it simply being the wrong modality and/or points for you - which is a possibility as not everything works for everybody. What comes to mind initially, as I've seen it before, is that you might be holding your breath too much and overfocusing on the tapping of points. Generally EFT, and any other energy healing technique, is relatively relaxing. It may not always be effective, but people generally do not get agitated. Holding your breath is one way of doing this and it is common in yoga, tai chi, acupressure.... all the healing arts. Another possibility is that you are wired a little differently. It's somewhat rare, but I've treated more than a few patients who have responded almost exactly opposite from the response that the vast majority of people experience. With these people it took some work, but we eventually found the right combination of points and directions to work with their issues. In that case you should probably book a few appointments with a licensed acupuncturist and have them get you started, then use their recommendations for acupressure.
Outside of your heart rate going up when performing EFT you don't mention what you are trying to treat, so I cannot comment too much on points. Certainly any of the point selections in either the acupuncture for anxiety or acupuncture for insomnia sections should be helpful. Points such as LV 3, SP 6, KD 1, and some combination of HT 7, HT 8, PC 6, PC 7, and/or PC 8 are usually helpful. The heart rate can be calmed down by two general acupressure methods (and relaxed natural deep breathing will do it as well) - (1) is to use acupressure in the ST 10, ST 11, & ST 12 area to stimulate the vagus nerve which has some control over the heart, the other (2) is to massage down from CV 15 to CV 6 or a little further to CV 3 - here you can use small circular motions with your fingers as you move slowly down the midline of the abdomen. Tong Ren Therapy is the energy healing technique that we use and you may find that helpful. To start, you could read our introduction to Tong Ren Therapy article.