After I Run 10k I Get Nauseous And A Bit

After I run 10k I get nauseous and a bit dizzy. Feel dreadful. I think my blood pressure falls very low. am 72 and have been running rather slowly for 10 years but had a break last year when I had a fall and broke my jaw. Started running again this year and am running a 10k race on Sunday and expect it will take me about 1.30 -40 minutes. When I feel awful after the race am I better to lie down or better to keep walking around? I have seen both types of advice.