if the coughing is really bad, try seeing if you can get a prescription for tessalon pearls. on the one hand i think they're a placebo but on the other hand they have helped a ton when i have had throat issues, which happens to be why i refuse to look up what they actually are.
grits and cream of wheat are two of my favorite sore throat foods to eat. orzo and mixed vegetables, either plain or with some sauce are another easy option v[and if you have a ginger or a spicy sauce it's great so long as neither bother your throat]. honey lemon tea is also wonderful. gargling with salt water or double strength black tea can help some too.
for sinus pressure, are you taking anything with a decongestant in it? if you aren't check with your doctor and/or pharmacist about guaifenisin [it's the stuff in sudafed and mucinex] and that can help some. if you're not averse to saline rinses or neti pots, that's another thing that can help clear you out, but i'd highly advise doing those right before you take a shower. and if your head feels a little sloshy, try bending over and letting your head hang down for a few minutes. when you right yourself it can make clearing out your head a little easier. it doesn't always works, but it sometimes does wonders. warm compresses also feel nice on your face.
-google first. ask questions later.