"Ich soll meine Lehrerin eher fragen."
"Sooner" versus "rather" makes a difference in meaning here, at least in US English. "Sooner" is generally a time reference (although some dialects do make it synonymous with "rather.") In this case, it would mean "I am supposed to ask my teacher [sooner than you want me to, sooner than some impending date, etc.]." Does "eher" lean one way or the other in German, or would it depend on context?
It depends on where you put the 'eher'. "Ich soll eher meine Lehrerin fragen" = "I'm supposed to rather ask my teacher (instead of the janitor whose advice wasn't that accurate)". "Ich soll meine Lehrerin eher fragen" = "I'm supposed to ask my teacher sooner" (e.g. if in the past I didn't ask any questions about a topic and therefore got totally lost. When I finally asked my question, it was already too late... so much stuff I had missed because I couldn't follow. So, in future I'm supposed to ask her sooner)
It hasn't been answered here yet, so I will try my best: 'I should' is not accepted here, because 'should' infers doubt, hence it uses the subjunctive II, much like could, would, etc. Hence, "Ich sollte meine Lehrerin eher fragen" = "I should ask my teacher sooner". I think in that case 'instead' would work better than sooner, it doesn't quite sound right to me.