For instance, if I want to search through all the identifications I made for emperor penguin, or any particular species.
You can use the identifications search interface, which has some filters but less than the Explore tab. For example, here are your emperor penguin IDs:
You would replace the taxon_id with the species (or higher taxonomic level) IDs you are looking for.
Or if you wanted the explore view instead of the identify view: https://www.inaturalist.org/observations?ident_user_id=chhang
There’s a very nice search tutorial wiki you might find useful https://forum.inaturalist.org/t/how-to-use-inaturalists-search-urls-wiki/63#heading--users--id
That will work for most cases but will only find IDs that match the current ID for the observation. If the consensus ID is macaroni penguin and cchang’s ID is emperor penguin then it will not find those IDs.
Instead of taxon_id=nn try ident_taxon_id=nn in there. It will bring up anything with you as id’er and the relevant taxon as an id, even if that’s not the current id. Unfortunately included in the set are records where you weren’t the one who did that id, but hopefully it won’t have too many of those “outliers” in the set.