Anaemia is low iron levels in the blood, which reduce the red blood cells' ability to transport oxygen around the body. It makes you tired, dizzy and breathless. If you had blood tests in the E.R. then they may well have already tested for it.
Some drugs cause a low blood pressure as a side effect; that can give you dizziness that occurs on going from sitting to standing, or lying to standing. That kind of dizziness is transient - once you've been upright a couple of minutes it passes.
Sinusitis can also cause dizzines and if you do have an infection there that would certainly make you feel unwell. Sinusitis typically gives you a headache when you bend over forwards.
For sinusitis/cold symptoms you could try inhaling steam, especially good with menthol crystals in or olbas oil, if you have any. Eucalyptus also good to put in the steam. When my sinuses are really bad I also just sniff the steam from a hot drink (or just hot water), as that's easy to do in bed! If you do have a cold/sinusitis type thing right now (which the hospital seems to have said) then you've probably also recently had a virus and that could also give you tiredness. When I have sinusitis and the heavy eyes that go with that, lots of steam really helps relieve the associated headache - faster than paracetamol in my case.
Try to find out if anyone has checked your bloods for anaemia and also check for low blood pressure on the list of side effects of any medication you are on. Meanwhile try some steam as that will relieve any sinus trouble.
Hope you feel better soon.
New stuff: GERD. Interstitial Cystitis
Lifelong stuff: Food allergies, eczema, asthma