Please read this post by clinical psychologist Dr Psych Mom - the title is about women dismissing men's frustration with lack of physical affection, but it applies to men too: When Women Consider Physical Touch To Be A Less Real or Important Love Language. I'll copy an extract here.
The woman (or the lower libido partner, which is more often the woman in a long term monogamous heterosexual pairing) often feels one of the following ways about her husband’s physical touch love language:
(1) Physical touch, especially sex, is like the “bells and whistles” on top of a relationship. It is not necessary, but is a nice add on.
(2) Physical touch, especially sex, should never be something you try to get in the mood for. That is icky and smacks of nonconsent. It should arise organically.
(3) Physical touch outside of sex is nothing that anyone “needs.” Sexual release itself may be a need for a man; therefore, any sex that is provided, even unenthusiastic duty sex, can meet this need.
It is interesting to think about how this would look if it were the woman’s verbal affirmation love language being discussed. What if the husband said:
“Saying nice things is the bells and whistles on top of the relationship. She shouldn’t need it. If I’m not in the mood to be nice, it is gross for me to try to make myself say nice things. She shouldn’t want me to force it. If anything, I can say, ‘You look nice today’ in a flat, dull monotone with no eye contact and this can meet her need for verbal affirmation.”
....
This... puts the partner whose love language is physical touch in a one-down position in the relationship, where they are made to feel that their needs are less real than the other partner’s, or that the other partner’s needs should be met before theirs are even considered.
Imagine a parent saying, “My child loves to hug me, but I prefer talking. Therefore, I routinely deny, minimize, and even mock her need for hugs and initiate long conversations about how she feels about me, her, and our relationship as mother and daughter. If she talks for long enough, I will give her a quick hug at night, although sometimes I tell her that her hug quota for the week is already met.” This would be considered sadistic and emotionally abusive
She has some great podcasts on related matters which others on this board have pointed me towards, eg look up Dr Psych Mom podcast "Yes There Should Be A Sexual Marital Contract ". She's fun and informative to listen to. One point she makes in the podcast is, would you want your children to continue visiting a friend who routinely misled them or denied their needs? Lack of sex is absolutely reason enough to leave, if it's important to you. Would you want your children to live in relationships where they were routinely rejected and felt unloved, by the one person who was supposed to love them and find them attractive? I had years of lying in bed alone while my husband drank downstairs, wondering if I was really that unattractive, thinking that surely somebody else would love to have me. But I didn't see a way through. Well, it turns out that there was a way through and I've got a new lease of life. The teenage children have commented that they can see their father and I are both happier with other people, even though we never used to row.
Your husband needs to know that this is serious. Put your cards on the table. If your partner values you, he can go to the doctor and to a sex therapist to try to solve the problem. That's what putting the effort in looks like. If it doesn't help, at least you'll know he had the chance to try. But please don't sell yourself short and settle for this when you're so obviously unhappy.