Frustration... waiting times

Hello, I’m 32 and visited my gp 5 weeks ago to report a very obvious lump near my armpit.
I was referred to the breast clinic.
It took until yesterday to be seen.
I was told that I’m too young for a mammogram, so will now need to wait two to three weeks for an ultra sound slot to become available.

Is this a normal amount of time to wait? Why didn’t anyone notice my age before this breast clinic appointment?
I feel a bit silly as there are people here facing far worse problems but I’m just frustrated and want to know what this lump is.
Any advice?
Thank you.
Emma.

Just to add, I’m in Scotland. Not sure if that makes a difference.