I tried many things from this post
- Go to airplane mode for some minutes
- Fix the date and time
Nothing fixed the problem I had.
But I managed to fix the problem with this:
One thing I noticed when I went to Settings is that I didn't have the Carrier option. I didn't either have the IMEI info in the About section. I thought this had something to do with my SIM card.
So, I turned off my iPhone, took out the SIM card and put it in an old iPhone that I was not using. I turned on the old iPhone with the SIM card inside and the old iPhone asked me to unlock my SIM, asking for its password (something that didn't happen in my current iPhone even if I rebooted the phone). So, I put the SIM password and the old iPhone did get a cellphone signal, 3G signal and started working fine. At this point I had probably "re-unlocked" the SIM card, I guess.
After this, I turned off the old iPhone, took out the SIM card and put it on my current iPhone. Then turned on the current phone. The phone said "SIM locked" but didn't ask me for its password. I waited a few seconds and the phone was displaying "No service" (which was different from the previous "Searching" message). I went to Settings and I noticed that the Carrier option was now there, so I selected the Carrier option and then the phone let me choose the carrier for my SIM card .
I hope this helps someone out there with the "Searching" problem.
Long story short: take out your SIM card, put it in another iPhone, unlock the SIM card and then put it back to your iPhone. Go to settings and select your carrier.