"A&E visit after 3 hours wait for paramedics"

I called in 111 at 10:00 pm after my one month old son was crying continually for 1/2 hour, gave all details said they paramedics will arrive in 50 minutes

After 1&1/2 hours waiting first responder turned up and said paramedics will arrive soon and after nearly a two hour on continuous insistence they called paramedics and they said us to visit the queen medical A&E

When arrived at A&E nurse took all details and insisted another wait finally Seen the doctor who said they had not gone through the notes and does not his current temperature and other things rather was asking me about it, on just visual inspection sent us back saying everything is fine

I will was this why to waste our time they said the same at first instance when the first responder done the temperature and other checks

No proper check done, had wait for paramedics for 3 hours not at all acceptable

To avoid they could just have said us to visit A&E in first place