Marc P. answered 08/04/19
Ivy League Grad to Help with Standardized Tests and Academic Work
Your native intuition is correct. Generally, we use the definite article to indicate specific items. I'd say that you could include or delete the definite article in the first sentence you cite. However, since you are talking about a specific spring semester (the one of your junior year), I would include it.
In the second sentence, though, it is clearly incorrect to write, "One graduate course had been sufficient to consume my time fall semester." Sometimes we use nouns as if they were adverbs in order to indicate time; for example, the following sentence is correct: "I will succeed one day." In that sentence, the noun phrase "one day" is used as if it were an adverb (modifying the verb). However, "fall semester" seems to refer to a specific time period and can not be used adverbially. It is better to write, "in the fall semester".