yeah you should be proud of both scottish and english heritage.
the scottish were tough and have beaten the english many times(vice versa aswell) but they did get taken over by the english, the scottish beat the english for independence but the reason they won was down to the english forces been spread across Scotland, Ireland, Wales, North of France, and even other parts of Europe because the Normans were claiming and invading land everywhere and used the english soldiers to defend their land. so thats where the whole rivalry came from.
the scottish fought back the romans aswell and had conflicts on more than one occasion with a common enemy of both the english and scottish... the vikings.
also you are British... ever heard of the Black watch? a lot of scottish in the armed forces and special forces today.
trust me, seeing as you are half english, half scottish you have the best of both worlds (aswell as being British).
its the wars that Britain ahve been in where the scottish and english have fought alongside eachother... they are the wars to be proud of hehe.
so tell your friends to piss off.
edit: oh yeah people are mentioning scottish inventions... look up the "scottish enlightenment". thats an example of how great the scottish are/were.
edit: one of the greatest men in history, King James of Scotland is the guy that formed Britain.