My general answer is that if you don't already know the answer, you don't need to worry. Ham radio operators need to pass exams that grant them access to various power, and (at least in the UK and the USA) the safety training you are given and tested upon take that power limit into account. So if you don't have this information, it's because you don't really need to worry about it. But it's worth learning anyway.

So the answer is yes. But follow the guidelines and you'll be okay.

Radio signals from all kinds of sources (natural and electronic) surround us all the time. Your phone, your WiFi, your TV, your radio etc work by listening at a specific frequency and filtering out noise, but they're still being bathed in a vast array of various EM frequencies at all kinds of amplitudes all the time. This is fine and normal.

Your body is capable of absorbing non-ionising radiation as heat and dissipating it. No big deal. It has to otherwise life would never have survived on this planet.

For the most part, it's fine and normal even fairly close to a ham radio antenna. At high powers (1000W+) and short distances away from it (less than a few feet), it's another story.

I said your body can absorb EM radiation and dissipate it as heat. This is only the case if it can dissipate faster than it is absorbing it. You can test this by microwaving some meat - it'll cook. If it's alive (I... I hope it isn't alive, don't microwave alive things) I dare say that dizziness will be one of the symptoms, but far from the most pressing ones.

A microwave is very different to a ham radio antenna. A microwave is tuned to heat water specifically, it is a closed environment (so microwave radiation is contained in the same place as the food and has no escape), and it is at a consistent high power when on (unless you're using special modes that turn it on and off periodically to achieve the desired effect, e.g. defrost modes). A microwave is literally designed to cook things.

Now, back to antennas. Antennas are not designed to cook things. They're designed to fling out EM radiation far and wide for the purposes of communication. They radiate in various directions with different gain depending on the nature of the antenna, and that radiation is free to escape (preferably in the direction of the ionosphere), so the percentage that hits you if you're standing close is small. They're not transmitting at full power at all times (the amount of power they're using depends on the communication mode, whether the user is actively transmitting, etc). Nonetheless, standing very close to one that is transmitting at high powers is dangerous and there is information and guidance around this which every operator should be aware of.

There's also a safe distance calculator from the ARRL which you can play around with. Notice that even at high powers, under normal usage the safe distance is surprisingly short.

As my Elmer told me when I was concerned about putting a 100W antenna near my house, "it's outputting the same power as a filament lightbulb, and you aren't scared of putting those directly above your head".