If you checked or chametz properly and said Kol Chamira you did not transgress anything. When you found the chametz you should have burnt it otherwise there was problem of Bal yiraeh. It is a good idea this year to make a list of where each piece of bread is placed to not have problems.
Explanation:
There are two obligations by Bedikat Chametz. One is to check of the Chametz and the second is Bitul Chametz, nullifying it.
The Mishna in Pesachim 2a : The night before the fourteenth one must check for chametz by candlelight.
The Gemara 6b: Rav Yehuda in the name of Rav said, after one check he must nullify his chametz as well…Rava explains the we are worried one might find a rugelach( piece of chametz) and want it.
Rashi explains that it is important in his eyes and eh will not want to burn it and keep even for a split second he transgresses Bal Yeraeh, but if he nullified it then he doesn’t transgress it.
The obligation to check is either because -Rashi so he won’t transgress Bal Yiraeh. Tosfot asks but then its same thing as bitul, just do bitul? The Ri explains that you should not come to eat chametz by mistake.
Rashi is of the opinion it is because of Bal Yiraeh.
The Ran writes: Since one fulfills his obligation to not have Chametz from the Torah through Bitul, nullification, and the checking is rabbinical in nature maybe you’ll come to eat chametz on Pesach, however the Bedikah with a Bitul will work to fulfil the Torah obligation and if he checked thoroughly even I he finds Chametz during g Pesach you will not transgress Bal Yeraeh.
The Ran also says even if the Bedikah is Rabbinical the reason for the bedikah is that we are worried about transgressing Bal Yeraeh since the Bitul depends on what a person thinks, maybe not everyone nullifies with everything completely willingly.
According to the first answer Rashi agrees to Tosfot that if he did a nullification then the obligation to check is only Rabbinical. only if he didn’t nullify is it from the Torah.
(The Chemdat Shlomo OH siman 4 asks what is the worry that he won’t nullify the chametz completely, the whole reason why Chazal require Bitul is because they are worried if he finds a nice piece of Chametz he might hesitate to burn it, why not worry first that he didn’t do a good bitul? He answers the worry that he won’t do a proper bitul is only if he doesn’t do a bedikah, then we are worried he is trying to keep chametz around and he won’t do a proper bitul.)
What comes out is that you need to do both Bitul and Bedikah and dong one of them is enough to exempt one from Bal Yeraeh. It is not enough to just do a bedikah because maybe he missed some chametz and he will find and hesitate to burn it and transgress Bal Yeraeh, therefor he must do a Bitul. If he only did a Bitul he won’t do a full bitul and therefore if eh finds chametz he might come to eat it therefore you must do a bedikah and burn all the chametz. So writes the Mishna Berura 431:2.
Therefore, since you did a proper bedikah and you really looked for the Chametz, then you did not transgress Bal Yeraeh. However, after you found it you should have taken it out quickly and brunt it.
The Gemara in Pesachim 6a “Rav Yehuda said in the name of Rav one who finds chametz in his house on Pesach, on Yom Tov he should cover it with a cup (until Chol HaMoed).
The Rishonim argue if cover it it is only if he did Bitul and therefore they do not transgress Bal Yeraeh but if he didn’t nullify it then he should pick it up right away and throw it in the river and we permit muktzeh for this. (Some say to burn it). This seems is what Rashi understands. The Rambam however (Chametz UMatzah 3:8) understands that even if he didn’t nullify, he can’t destroy it on Yom Tov and he is to even permit to move it since it is Muktzeh (Mishna Berura 446:6)
The Shulchan Aruch 446:1 writes: one who finds Chametz in his house on Chol HaMoed should destroy it immediately and if it is Yom Tov, he can cover it until the night and then burn it.”
The Rema adds since it is muktzeh n Yom Tov he can even burn it its place.
Since the Shulchan Aruch doesn’t differentiate whether he did a Bitul or not in any case he is allowed to cover it on Yom Tov. on Chol HaMoed he must burn it.
There is an argument brought by the Mishna Berura 435:5 if he needs to make a new blessing of al Biur Chametz and w say that Safek Brachot Lehakel.
Therefore, you should have taken it outside and burnt it (Or flushed it down the toilet) not thrown it into garbage.
This year be sure you write a list where the ten pieces are being put through.
