。
I felt like I was being watched.
Literal
I [topic-は] watched-being [resemblance-ような] feeling [subject-が] did.
見張る (みはる, 'to watch, keep watch') in passive ~られている ('being watched'). ~ような気がする ('feel like, get the feeling that') expresses a subjective impression. Combines passive + ongoing + resemblance + feeling — a layered construction.