Should I include country dummies when I combine datasets of 3 countries?
I would advise you to think deeper about your research question first, as this will guide the decision to use country fixed effects. If you would like to exploit cross country variation, for example by studying how the same industry functions differently across countries, then do not use country dummies because it will absorb the variation you want. 

If you want to study a causal relation that is independent of country, then using "within-country" variation (i.e. include country dummies) is the most restrictive approach and will sweep out all fixed country characteristics. Your coefficient will then be identified off deviations from within country means. 

Are you sure that countries are similar across most characteristics in order to defend not using country dummies? It may be hard to defend solving omitted variable bias on those grounds. If you really want to go this route, then include several country covariates as controls.