Yes it's a hard one as when one is desperately seeking everyone does seem to be too busy to admit new people into their lives. It's well worth seeing a therapist to see if there is anything you are doing wrong but it could well be that you aren't.
Try participating in activities that you really enjoy where you come in contact with others. Then you have something in common and you won't feel as disappointed if nothing eventuates friendship wise. Targeting ongoing activities where you see the same people is good as you don't have that pressure to pounce on someone too soon but can let the connections naturally build. You also gain a sense of the other people so can plan and target invitations in a way that you are more likely to get a yes.
I've found acceptance and commitment therapy/mindfulness helpful as it's not about "challenging" your thoughts around your experience to prove that it is just "faulty thinking" but is aimed at helping you live with a not ideal situation that is difficult to change by making your thoughts/situation less painful. But ACT also encourages you to get in touch with your values and make changes in accordance with these.