Hi anna. As Babcock_Hall mentions, there is a lack of detail in how you'll go about with your transformation. I think this is also a matter of strategy and choosing which transformations to attempt first.
Methanol with some auxiliary acid/base will definitely not methylate an amine and you'd likely only get esterification with those conditions.That being said, you'd be able to esterify your carboxylic acid with benzyl alcohol easily without methylating the carboxyl group first.
Perhaps also think about what other reagents could yield a methyl equivalent for reaction with the nucleophilic amine, as methanol is a poor electrophile. Also, carboxylates/carboxylic acids are very poor nucleophiles so you'd find that by selecting the right electrophiles you could avoid reaction at the carboxylic acid - that is if you decide to do the methylation prior to esterification.