I wouldn't feel dumb for not checking them first, for both bulbs to go bad at the same time is sorta unusual so most would think it was something else like a relay/flasher/fuse, etc. and not the bulbs.

When something like this happens to me I just test everything before buying any parts, Youtube is a great resource for many things if you're not sure how to test or do some procedures, just be sure to check several Youtube sources since there are some people posting videos that sometimes don't really know how to do somethings correctly which could lead to other issues.

Issues like this is how to learn things you don't know from those with more experience and what this forum is all about if you ask me!