You are right that 上 and 下 imply past and future, and these can pretty much be used before any noun specifying a time： 周、星期、礼拜 (all meaning "week", in ascending order of informality)、 次、回 (both meaning "time")、 学期 (semester), etc. Numbers 1-6 or 天/日 can be placed after the words meaning week, as such: 上星期三 (last Wednesday)、 下礼拜天 (next Sunday), etc. Using 上/下 with 周 admittedly sounds a bit weird, so I would stick with 星期 for "week".
For other time-specifying nouns, such as the following, 上个 and 下个 can be used: 月 (month)、周末(weekend). In these two, the measure word 个 is optional, but can make the phrase sound a bit less awkward. Of course, with other nouns, the measure word should adjust. For example: 下一场球赛 (the next ball game). The 一 is used here to specify that the phrase refers to the next one ball game, as opposed to, for instance, the next few: 下几场球赛. This quantifier usage is more common for these "other" nouns (basically the ones that don't deal with basic units of time defined by earth's rotation and revolution).
For 天 (day) and 年 (year)， however, 今 (current) and 明 (next)， and by extension, 前 (one before previous) and 后 (one after next), should be used. For "previous", 天 takes 昨, and 年 takes 去.
In general, Chinese grammar rules are not as strict, but word usage is. Make sure that you use follow the rules in the last paragraph to avoid usage mistakes. For example, use 昨天 for "yesterday" and 去年 for "last year" instead of getting them mixed up or even using 上 or 下.