Most of the time, yes they will find those prior claims.
Many insurance companies participate in a national database that tracks claims. They will also check you MVR records of any tickets or accidents. It is very difficult to slip one past an insurance company.
Fraudulently stating fewer claims than you actually have is not a good idea. If you filed another claim and the prior ones were discovered, they could deny the new claim, back charge you a higher rate, and/or cancel the policy on the spot.
Because your rate went up due to the claims, it's not a bad idea to shop around, just make sure they are rating you with knowledge of those prior claims.