Lee I am lucky enough not to know much about 3rd degree tears except they are pretty awful.
You have a couple of problems here really; first is her fear following the 3rd degree tear (she may even be terrified of getting pregnant again consciously or subconsciously)
there is the loss of her sex drive which is very common after a baby - due to tiredness
and a the rest of it- and quite often the less you have sex the less you can be bothered to do it.
then there is the problem that she has devoted herself to the baby and forgotten about you and the relationship (this is very easily done and very, very common)
It is all awful for you and you have been patient and lovely about it, by all accounts.
Putting pressure on her to have sex won't work but, if she loves you, she should be prepared to show you some affection and talk to you. The problem often is, in this situation women (and men) are afraid to engage in affectionate behaviour in case the other partner takes it as a green light for sex.
Why don't you write her a letter? tell her how much you love her and the baby and your new lives together but that you want some of your old relationship back, remind her of what it used to be like and say what you miss like mutual affection, going out together, etc. Ask her to spend some time alone with you (on the understanding that there will be no sex) get dressed up, go out for drinks, talk about something other than the baby, have a snog etc. and go from there.
If she was willing to give sex a try, maybe when you take the pressure off, she might lose her fear of it.
You could also ask her to see the GP perhaps?