Yes, "I need to go to the pet store, and I need to remember my bag." is a compound sentence because it includes two independent clauses joined by the coordinating conjunction "and."
is "As im going to the pet store, i need to remember my cash." a complex sentence?
Yes, "As I'm going to the pet store, I need to remember my cash." is a complex sentence because it consists of a dependent clause ("As I'm going to the pet store") and an independent clause ("I need to remember my cash") joined together.