回答
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I thought there was a lesson today too.
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I thought I had a class today as well.
「今日も授業があるかと思ってた」はこのように言います:
(1) I thought there was a lesson today too.
(2) I thought I had a class today as well.
「と思った・と思っていた」はI thought(thinkの過去形)と言います。
「授業がある」はthere was a lessonまたはI had a classとなり、どちらの場合でも過去形になります。
「も」はtooでもas wellも使えます。