colds can set the stage for secondary (bacterial) infections so yes. it would be wise to see your medical provider to be examined diagnosed and treated. colds last a week so when someone tells me that they are (a) getting worse after a week and (b) coughing blood there is a clear indication to seek some hands-on medical care.
i've had a cold for a week the cough seems worse than when the cold first started i'm also coughing up some blood. also when i blow my nose there is blood in that also should i see a dr.