Are you using browser-based forms or the InfoPath rich client? If you are using browser-based forms, look at the InfoPath Form Web Part that shows the form in a web part. You can use two of these web parts each pointing to different forms and you can have the dropdown set a value to control what gets displayed in the second web part. Another idea is to use two views in the same form and have the web part display the same XML but with separate views. Then, you don't need to do as much wiring to get them to display.
If you are using an InfoPath rich client, you can use the NewFromSolution action to open a new form based on a dropdown event. Double click the dropdown and go to properties, rules, and add a rule with an action that does that.
Publishing to SharePoint can be done without code. File->Publish is your friend.