My guitar doesn't have a truss rod.
And yesterday I changed my strings and took a higher gauge (from 0.09 to 0.10)
Can this cause any damage to my guitar?
Your guitar probably does have a truss-rod, but it might not be adjustable.

Heavier gauge strings do require more tension, but 10s are still considered light.

I wouldn't worry.
Quote by Jackal58
I release my inner liberal every morning when I take a shit.
Quote by SK8RDUDE411
I wont be like those jerks who dedicate their beliefs to logic and reaosn.
electric or acoustic?

if its classical then thats fine aslong as you're using nylons.

otherwise im not sure, its not a huge step up. Aklso if your guitar has a strat style or floatring bridge then it may need adjusting.
Quote by Nosferatu Man

T-shirts are a sign of degeneration and decline.
It's a Washburn X-10
I changed them about a week ago, I think, and there's nothing wrong with them.
But if someone has some more advice, tell me!
(Like, do I have to change the intonation?)