Panic attacks are usually psychological in origin, although they do occur with several medical conditions which cause excessive release of adrenaline. You are right, they are terrifying and extremely unpleasant. But your baby simply does not have the psychological wiring yet to have an actual panic attack, so look to other causes for this. It is either a medical condition (and I strongly recommend that you speak with your baby's health care providers about this until you have a satisfactory answer) or is a sleep disorder. I would place colic under "medical condition".
Please read about night terrors, also known as Sleep terrors. See if your baby falls into this pattern. (He is a bit young, but it's a possibility.) To do so well, you'll need to keep a sleep diary, which is not a bad idea in this case whatever the reason.
A baby experiencing sleep terrors does indeed appear to be in a panic, but it is very specific in its patterns.
It might be that the baby is still experiencing startle reflex, aka Moro reflex, which awakens him and leads to his crying.
Another, more dramatic reflex during these first few weeks is called the Moro reflex. If your baby’s head shifts positions abruptly or falls backward, or she is startled by something loud or abrupt, she will react by throwing out her arms and legs and extending her neck, then rapidly bringing her arms together and she may cry loudly. The Moro reflex, which may be present in varying degrees in different babies, peaks during the first month and then disappears after two months.
This is why swaddling helps babies sleep more soundly. If the infant can't throw out his arms, etc., it will greatly decrease the reflex. (Imagine if you were startled by a loud noise while lying in bed. You might jump considerably. Now imagine someone has you wrapped in their arms. You would still startle, but you wouldn't jump as much.
Although the Moro reflex does start to diminish starting at two months, it can persist for another month or two, and if it persists longer than that, a doctor usually starts to evaluate the baby for other problems.
Colic is a distinct possibility, and many babies experience colic. The exaggerated fear you describe is not present in colic; it is 'just' inconsolable crying (as if 'just' can be a consolation; it's not!)
Infantile colic is an ill-defined condition which seems to consist primarily of pain associated with symptoms ranging in degree from general fussiness to paroxysms of agonized crying. The symptoms usually start after feeding and are worse late in the day. Besides the typical unhappiness, as exemplified by clenching the fists and flexing the legs, the infant often makes sucking movements and appears to be searching for food. Usually these infants have a great deal of gas, manifested by excessive belching, flatus, and rumbling. The passage of gas is occasionally followed by temporary relief, supporting the theory that distended loops of intestine from collected air causes colic. It is most common in the first born, usually starting at 2 to 4 weeks of age, and lasting through the third or fourth month.
The timing isn't consistent with colic, but not all colic is created equally.
So you see, we can't tell you what is happening with your baby, we can only offer some possibilities. Try swaddling, keep a sleep diary, if he is breastfed, pay attention to what you (if you are the mom) eat, etc.
Above all, talk to your doctor. If it is colic, they may prescribe drops for the baby.
You can be reassured that the baby is not afraid of his surroundings. Improvement of visual acuity happens to every baby, but not every baby goes through what yours is experiencing.