Yes, うち means "our home/house/office/etc". If there is no context, this うちの上の学校 should just mean うちの上にある学校, or the school that is located somewhere above their house. Is there a hill around their house?
Another less likely possibility is うちの上の子の学校, or the school which their older child attends. 上の子 means "the older child", but when there is no chance of confusion, 上 by itself sometimes can represent 上の子 (e.g., うちは上が8歳になりました). But this interpretation depends on the context. Unless they have been talking about their kids, this interpretation is not very likely.
EDIT: Checked the actual game clip and the basic setting of the game described in Wikipedia. It's probably "the school one stage higher than ours" as broccoli suggested. But this is indeed a roundabout and puzzling expression — why didn't he simply say 高校 or something? Well, although she might look like a 女子高生, the author probably did not want to explicitly mention what type of school she attends, as this was an eroge and her age must not be specified. If you happen to know why the term 女子校生 is often used in eroge, this seemingly weird expression is in the same vein.