How to cope with an anxious attachment style in relationships and stop getting so upset all the time
Sounds like you are blaming anxious attachment on your tendency to get extremely upset over the smallest things. I guess I would need to talk to you one on one to see what is really going on. That would not have to be me, but you would probably be well served to get actual answers via actual time with a therapist. Anxious attachment is not the same as overreacting. Anxious attachment means that you are very nervous about the relationship not working. Anxiously attached people fret and worry that the relationship is going to end and they are going to be abandoned. Are you worried about abandonment?
A therapist would be interested in knowing the specifics behind the reportedly small things that you are getting upset over. I would ask that question. Maybe these things are not as small as they seem? It is hard to know. Often times we have emotional reactivity because it actually does matter. Could you be discounting your perspective. Maybe your partner is not meeting your needs? Again there are a lot of things to explore in therapy.
Attachment has more to do with the other person than ourself. Recent research around attachment actually indicates that attachment is more to do with specific individuals than a universal attachment. You are not likely anxious with everyone. What is it about this relationship that makes you anxious. Also another good question to have explored in one on one therapy.
Another thing that makes me wonder is that you say your partner is not a very emotional person. Actually are they not emotional or are they not emotionally intelligent? Again, as with most of this answer it is all speculation. Perhaps you and your partner would like to explore both of your emotions in couples therapy.
Sounds like you and your partner are trying to make the best of a long distance relationship. That arrangement is not impossible but it is very stressful. I wonder how long you plan on doing the long distance relationship. Long distance relationships can be very difficult to sustain.
I think that the best bet for getting clarity on these issues is to do either couples counseling or individual counseling. It may not be you, it could be a lot of other issues that are not apparent.