Yes, you're right But "sollst" in this context stresses that there is a command from another person involved, as in:
Deine Mutter hat angerufen. Sie sagt, du sollst nach Hause gehen.
Whereas in this sentence, you most likely wouldn't use "sollst":
Oh mein Gott, ich muss schnell nach Hause, wir hatten einen Wasserrohrbruch! (... We had a water-pipe rupture.)
"Sollte" can be both past tense and subjunctive of sollen - which it is here, as subjunctive can be used to express advice. So "sollen" becomes "sollte" in the past tense.
Ich war wütend auf mine Mutter, weil ich schon um 9 nach Hause gehen sollte. ( I was angry with my mother because I was supposed* to come home at 9.)
Because they are two forms of the same word, "sollte" doesn't have its own past tense form.
*can I say it like this? I'm never quite sure how to translate "sollen" into English