I got my first covid vaccine 3 weeks ago and immediately felt hot in my neck, had a slight rash on my neck, and felt a little dizzy. it went away in 20 minutes. i haven't been able to find similar reactions online. is it safe to get my 2nd dose?

Yes. This is common (and usually not serious). Inform the center about this when you get the 2nd dose (and be prepared to stay there for ~30 min to make sure you stay ok)

Everyone reacts to vaccinations (not just The Covid one) differently, and some reactions are more common than others. Your reaction was not severe enough to warrant skipping the 2nd dose. Let the clinic know you felt dizzy after the 1st shot, so they can watch you more closely afterwards. Rest until the dizziness subsides. Make sure you are not hungry or thirsty before getting vaccinated also.

Based upon your post-injection response, see absolutely no reason NOT TO GET your second injection and indeed you will need it for optimal immunity. Do not fear, but yes, ask for at least 20-30 minutes of supervision.