What is the most widely accepted EMF exposure limit?
You mentioned that there were some cell towers near where you lived, however, they are unlikely to be providing much of a discernible signal (-90dBm is considered a 'good-ish' cell signal and corresponds to 1 one billionth of a milliwatt, mobile phones don't need much signal so there's no point having the tower waste power by blaring away at full power - that would drown out the received signal anyway). The vast majority of your detected EM radiation is likely from and commercial Radio or TV stations nearby. A cell tower might pump out a few tens of watts if it needed to talk to a far away phone, but a TV station could easily be dumping 50'000 watts into the air (megawatt class transmitters are not unheard of - The Fernsehturm Berlin TV tower was the first Wikipedia result for "TV tower" and that does... or used to do a million watts or +90dBm on channel 27 - one million trillion times more powerful than what you might call '2 bars of reception')

The electromagnetic spectrum is quite a crowded place and has many bands, we have
ELF (lightning, tectonic motion - yes that does generate some Electromagnetic energy) 50/60Hz from the mains (a hundred km of mains cable makes a good antenna)

HF/VHF which covers just about all common commercial radio and TV broadcasts (which are broadcast at power levels several thousand times stronger than that from cell towers - we don't hear about those though, strange isn't it?)

UHF which sports the TV channels that didn't fit in the VHF bands, some of the bands used by mobile phones are also in the UHF band (some are actually squashed in between TV channels)

Next comes the SHF band with phones, microwave ovens and GPS, wifi, bluetooth, cordless home phones, some garage door openers, wireless weather stations etc. at the lower end while satellite TV, some security motion detectors, SATCOM, RADAR (be it automotive, weather, military, aerospace etc.), most emergency and military radios along with the microwave repeaters used both by "on scene" news crews and by telecomms companies to bring telephones and internet to remote rural communities at the higher end.

Beyond that is the EHF band, more commonly knows as millimeterwaves and includes THz radiation which is really only used by radio astronomy at the moment (but may end up in airport scanners soon).

Now moving out of the radio realm and into the "light" bands we have Long Wave Infra Red (LWIR) which is just a fancy name for heat (but it's still EM radiation)

I'm sure you know how the rest of this goes (I may have left out a radio band or two somewhere but you get the idea)

The moral of this story is that A) the strongest EM source is probably a TV station and not a cell tower (by quite a wide margin) and B) the strongest sources of EM radiation have been running for far longer that cell phones have even existed, if Radio band EM was going to kill people... I think after a century someone would have noticed. It's the EM radiation in the visible band that you really have to worry about (and can be commonly found at levels of several thousand mW per m^2). If you have a microwave oven, it probably produces more EM on average than a cell phone unless you use your phone for hours everyday.