As Edwin Ashworth and Matthew Haugen said, "I panicked" and "I was panicked" are both grammatically correct. Both are in the past tense.

As user84593 said, "I panicked" is probably a better choice in most contexts. Edwin Ashworth left a useful comment:

The passive usage is admittedly far more common than the participial adjective usage ( panicked - AudioEnglish.org : Familiarity information: PANICKED used as an adjective is very rare.) However, 'I was panicked' is not incorrect. Compare 'We found that the window was broken' (broken: participial adjective) and 'The window was broken by the pigeon' (passive construction). – Edwin Ashworth

Grammatically, "I panicked" simply uses the intransitive verb "to panic" in the past-tense form.

"I was panicked" is more complicated to analyze. As Edwin Ashworth's answer indicates, in principle, it could be seen as either a standard "eventive/dynamic" passive construction, or as a "stative/static" construction where "panicked" can be analyzed as a predicate adjective. For a more detailed description of the differences between these types of constructions, see my answer on ELL to is “folded” a verb or adjective?

In either case, it could be followed by a phrase starting with "by" that indicates the agent or instrument that caused the panic.