I think the bike size should be fine. If the neck pain persists or worsens, then you might need to look at some exercises and stretching, but it could just be that you are not used to the position (putting your neck in extension while reaching forward and down with your arms).

Something that people sometimes do if they have persistent problems is flip the stem so it angles upward more, which raises the handlebars. For example, if you have a 110mm stem with a 6 degree angle, flipping it would raise your handlebars nearly an inch and bring them about a quarter inch closer to the saddle. This would result in less reach down and forward to the handlebars. Once you get used to that, you can flip the stem back down. Given that you bought the bike there, the LBS might flip the stem for you for minimal or no fee.