Hi Daniel and welcome to the project meditation community,
The 'panicky' feeling is something being created by the mind, not your real Self. The fact you are aware of the panicky feeling means you can't actually be the panicky feeling, and that's a good indication that it's not real, but something created by the mind. If you like you can think of the mind as a naughty trickster, that creates fear for itself and actually believes that if you enter a deep meditative state, it will disappear for good. In a sense, the mind will disappear during deep meditation, but it will also return when we come out of the meditative state and that is what it fears won't happen. It is the mind's 'fear' that causes the panicky feeling, and it does that in an attempt to stop you from reaching complete awareness in the state of deep meditation.
Saying that, it's quite normal for this to be experienced. With practice, we can learn to observe the mind creating this feeling, be aware of it for what it is, and choose to carry on, as we know that it is nothing that can harm us. It's not something you can just avoid, but it's something you can expect and be aware of.
Hugs
Giles
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