I have 3 dead sparrows and even though it says right next to them I can appraise them, they don't show up in Montak's Antiquities.

How can I appraise the relic?

Dead Sparrows are a Pup Toy, and none of those can actually be appraised. Shards also can't be appraised, although the full relic might - for example, you can't appraise Pottery Shards, but you can appraise the full Greek Pottery.

In order to view your craftable relics, go to Relics > Craft. As for appraisal, if Montak doesn't list a certain relic as appraisable, then it cannot be appraised.

How do I use the Dead Sparrow?

Go to the pup, click manage wolf, use item. Select the dead sparrow from the drop down