sofierat, there is no law, or dictat, or guideline, or anything, that says you have to breastfeed in order to be a loving mother to your son :(
You can be a loving mother while formula feeding - and you can offer your son the closeness and physical connection that's so important to you, with a bottle - check out 'paced bottle feeding' for ideas on making bottle feeding just as responsive and 'connected' as breastfeeding.
It's important for both of you that you are comfortable and relaxed and that you feel good about yourself. There is no shame at all in what you are doing and if you ask your DP I bet he would be mortified if you thought he was disappointed in you. If he is, then he deserves a Big Kick Up The Bum....he may be sad with you, that things are not sorted, but he's not going to judge you unless he really is a grade A twat :(
I know not much at all about lip ties, so can't say whether this is a necessary or good value operation, sorry.
How about finding someone you trust to talk to in real life? Not someone who says you are making a fuss, and that it doesn't matter blah blah blah...'cos it clearly does, to you...but someone who will listen and support and let you be sad without telling you what you should feel or should do.
I hope things work out, and you and little ds go on to enjoy all your feeding times together, however the milk is delivered to him :)