Because you are already married, I think it's your duty to find undeniable proof that he hasn't had an affair. I'm not sure what type of messages he was sending her... I don't want to assume... but there is such a thing as a non-physical affair (aka emotional affair/infidelity). While lying about sending money to a woman only to later admit he was in fact sending her money is ABSOLUTELY shady, it's not quite "adultery"... which is the only acceptable reason for a divorce according to the bible.
Seek counseling with a credible pastor (or multiple ones). Take preventative measures from making additions to the family unless/until this matter gets resolved. You're completely justified in not trusting him at this time. He lied... and while he later admitted to it, he needs to understand trust can't be regained overnight.
As for people pushing you to consider divorce... they aren't the ones married to him. Continue to pray as you mention, and if he has been unfaithful, that skeleton will come out of the closet eventually.