It is unlikely that anyone would bar you from getting the second dose based on that reaction. While those symptoms are certainly annoying, they do not sound life-threatening and the risk of severe COVID is more dangerous.
Anecdotally, it seems that people who have a strong reaction to one dose don't have a strong reaction to the other dose, so maybe you won't have any symptoms at all following the second dose. Hard to say, but definitely inform your doctor or the pharmacist that you had an adverse event following the first vaccine.
I don't know about Moderna. But I can tell you about me and Pfizer. Four and a half minutes after getting my first vaccine I starting itching on my face which became red a swelling. Then being an asthmatic I started wheezing and finally anaphylactic reaction Epi pen used and off to ER. To make a long story short my physician said not to get the second dose. So instead two weeks later I got Covid after having first dose and had to wait 90 days to have an antibody test that came back positive my doctor agreed for me to get second dose under supervision of my allergist and taking 50mg benadryl administered by him and I had NO reaction with the second dose. Sorry to bore everyone with my story but it was one I really wanted to share. I am an asthmatic and cancer survivor.
Thank you guys. I informed them and they gave it to me. Drs said it was of no significance!