DSM-V (p. 195):
Selective Mutism
Diagnostic Criteria 312.23 (F94.0)
A. Consistent failure to speak in specific social situations in which there is an expectation for speaking (e.g., at school) despite speaking in other situations.
B. The disturbance interferes with educational or occupational achievement or with social communication.
C. The duration of the disturbance is at least 1 month (not limited to the first month of school).
D. The failure to speak is not attributable to a lack of knowledge of, or comfort with, the spoken language required in the social situation.
E. The disturbance is not better explained by a communication disorder (e.g., childhoodonset fluency disorder) and does not occur exclusively during the course of autism spectrum disorder, schizophrenia, or another psychotic disorder.


I don’t know if “can't say 'I love you' to family despite having a loving mom” means that you had selective mutism. The specific situation is intimacy and it interferes with social communication? But you probably made other remarks to your family.
Mostly it has to do with speaking at home, but not at school, mostly by very young children.
I think that only exposure therapy is not enough. Somehow you need to be exposed to talking, but it is very difficult to make a person with selective mutism talk. So beside exposure also a kind of cognitive restructuring is necessary: the best is to try cognitive behaviour therapy. Although Selective Mutism is said to be so infrequent that therapies aren’t tested very well.
I said very little in most situations and I just couldn’t get myself to say something, so I wasn’t exposed to the fact that I did talk. When I did say something I was for a long time bothered by what I had said wrong.
I wasn’t satisfied with not talking at school, but at very specific occasion something came to mind to say, I rejected that possibility. Afterwards I contrived remarks I could have made.
Later I did start talking. And at certain moments I worked quiet well. I did a kind of cognitive restructuring, I tried to train it and I also became less choosy about with whom I talked: I just had to talk during the breaks at the university with whoever that was possible.
Later I made less work of getting myself to talk, and my contacts became less. I also didn’t meet people with whom I could talk.
Starting at the university is an easy time to come into contact with other students. Also in the first years of secondary school did I talk with some class mates. I have been in four secondary school classes in total and when you switch to a class in which everyone has already made friends, making contacts is much more difficult.
Creating situations in which is it easier to talk with others is also an important element of getting yourself to talk.