Couple things you should do
1-do you have a blood pressure machine at home? If so, use it.
2-take your temperature
3-did you eat anything that may make your vomit look like blood? For example, did you eat red jello and then throw up? How much blood was there? Are we talking about a speck of blood or a lot? Anything more than a speck of blood(which could potentially be accounted for in other ways) means that you should go to the ER.
Since I know nothing about your history, assuming you aren't vomiting due to drinking, if you are over 50 or have any chronic health problems, you should go to the ER for some fluids - it would make you feel a lot better. If you are under 50 and in good health, you still may want to consider it if you are feeling that bad. It is pretty surprising how much just a simple bag of IV fluid can help. Especially since you are dizzy, you should consider the ER, as it sounds like you are significantly dehydrated (would cause low blood pressure/dizziness) and can't keep fluids down.
