Regular expression for words where the same symbol can repeat at most two times consecutively?
Every string over $\{a,b\}$ can be decomposed into runs of the same letter. For example, $$ abbaabba = a^1 b^2 a^2 b^2 a. $$
Since the alphabet is binary, the runs just alternate between the two letter. In your case, every run has length 1 or 2. We can distinguish between four types of words in your language, depending on which run is first and which run is last; additionally there are some corner cases. The set of words in your language in which the first run is $a$s and the last run is $b$s corresponds to the regular expression $((a+aa)(b+bb))^+$.

I'll let you figure out the rest.