Anxiety isn't exactly a condition that is associated with positive feelings and emotions. In fact, anxiety actually draws your attention to negative thinking, and can create a mental environment that is extremely prone to noticing only the negatives and overlooking the positives in nearly all aspects of life.
So it's surprising that anxiety has been linked to a feeling of euphoria. After all, euphoria is a positive emotion, and while it can be associated with negative things (such as euphoria from drugs or mania), the emotion itself goes against nearly everything we know about anxiety.
Anxiety and Positive Emotions
It should be noted that anxiety is often comorbid with other conditions, like depression. In some people, depression may lead to mania, which can lead to euphoria. Furthermore, some behaviors and addictions can cause euphoria as well.
Rather than think of euphoria in terms of positive emotions, it may be better to consider it the natural result of an absence of negative emotions. There are those that experience this rush of energy when an anxiety attack is over, or when they have a break from their anxiety. In some cases - although not necessarily common - the absence of anxiety can trigger this feeling of complete relief and happiness, as though you are ready to take on the world.
To some, that may seem like euphoria. But it's really the natural reaction to feeling like you're no longer overwhelmed. Euphoria isn't a bad thing, but it should be noted that this type of emotion without still looking for ways to cure your anxiety can have negative consequences, because you may become over-confident and stop using anxiety treatments only to find that it comes back.
Overall, however, it is not a negative emotion.
Euphoria After Panic Attacks
Panic attacks are severe moments of extremely intense anxiety that can be emotionally and physically draining. After the anxiety attack is over, some people report that they feel euphoric, almost as if their brain has decided to make up for the severity of the panic.
There is unfortunately very little evidence or explanation as to why this occurs. It simply seems that there are those that get a euphoria feeling once their anxiety has gone away. It is possible that it is the brain releasing hormones, like endorphins, as a response to temporarily overcoming the extreme anxiety. But it's just as possible that this feeling has no obvious explanation, and relates back to the idea that it may be a subjective experience after feeling the anxiety go away.
There is Not Necessarily a Need to Overcome Euphoria
If the euphoria seems to come with other worrisome symptoms, like signs of mania, then it may be something you need to treat. But in general it is simply a positive emotion that results from a significant amount of negative emotions, and not something you necessarily need to treat.
Still, the only reason you feel that emotion is because you've had to deal with extreme anxiety, and so obviously it's important to rid yourself of that extreme anxiety as quickly as possible.