I have never experienced an allergic reaction before.
Does it imply I'm experiencing an allergic reaction at the moment of speaking?
I have never experienced an allergic reaction before.
While it maybe could imply that you are experiencing a reaction at the time of speaking, it is unlikely. The scenario needs context to make that clear.
I had never experienced an allergic reaction before.
This sentence would imply that you have had or are having an allergic reaction. But again, it's slightly ambiguous and requires some context to fill in the gaps.
Now let's look at this sentence:
I had never experienced an allergic reaction before [time].
Alternatively: "until [time]"
Here's an example:
I had never experienced an allergic reaction before yesterday.
This tells us that you had an allergic reaction for the first time yesterday.
This sentence works with other time phrases as well, such as what you are looking for:
I had never experienced an allergic reaction until now.
This tells us that you are having an allergic reaction at the time of speaking.