I thought (in the middle of Shemona Esray of mincha) that I must count the first day of sefirah after I finish; but did not do it verbally. Should I continue on to make the brocha from the second day?
In Bei'ur Halacha in 489 s.v. Mone Veholech he writes that [even] if one [actually] counted in his heart he certainly did not fulfill his obligation, so normally one would count with a Beracha.
But in this case since you did not verbalize the count of the Omer at all that day - you wouldn't be able to count with a Beracha anymore especially since you didn't think "Today is the... day".
Definitely ask your Rav what to do Lehalacha!
Nitei Gavriel (Pesach vol. 3 33:3-4) writes that one must verbalize the count, and does not fulfill the obligation of counting just by thinking. In the event that one did count only by thinking one night, he may continue the subsequent nights to count with a brocha, since in this case we will take into account the opinion that thought counts as speech (Shu"t Agura Be'ohalecha 1:28). However, this is only in the case where he had specific intention to fulfill the obligation of counting by thinking; if not he does not fulfill the obligation at all and cannot continue counting with a brocha (Eishel Avraham Mibutash Siman 489).
In the OP's case, it seems that his thought was "I must count day one of sefirah when I am done davening", and not "I would like to now fulfill the mitzva; Today is the first day of Sefiras Ha'omer". Therefore, he would not be able to continue counting with a brocha.