General spelling rule: no double (repeated) consonant after another consonant?

English spelling has patterns, but no perfectly reliable rules. Even very common patterns such as your example have exceptions, to the bane of all.

A double consonant following another consonant is possible when the double consonant crosses a morpheme boundary, as in words like dumbbell or jackknife. This includes most of the obscure words or spellings claimed to feature triple consonants, like goddessship or crosssection (in practice, such words are generally hyphenated, goddess-ship, cross-section).

Another set of exceptions would be various representations of sounds, like psst or zzz. , though some might object to their classification as words.