DS got a diagnosis in 3 months but he was younger, more severe and had regressed. It took another 18 months to get decent support and intervention in place so don't feel you have to have a diagnosis before you can access help.
I would speak to school / SENCO as they may know about strategies already for ASD, or can find out / access support and any additional understanding at school can only help. Some ASD outreach teams will come in straight away but in some areas they will only come in once you have a diagnosis.
Tell family when you are ready. Family aren't always ideal in the initial stages as they have so much hope and expectation tied up in your children and can often go into the same denial phase you are just emerging from. My best confidant was a mum at school who when I said I was getting DS investigated just said 'why do you think he might have asd' and let me explain and just listened; instead of everyone else who said 'it can't be asd because....' or 'but my child does that too' or 'I heard of a child who didn't speak and then at 3 they spoke in sentences'. People don't know what to say and often are very dismissive because they can't cope with the subject matter. Sometimes you actually have to say (as I finally did to my mother) I don't find that helpful, I actually just need someone to listen to my worries. You find you become more thick skinned and tolerate less BS once you enter SN world. Sometimes you need to tell people how they can help you as actually thats what they want to do not make a hash of it.
You can ask for an occupational therapist to visit and assess safety and advise - usually the OT attached to social services not NHS (ie via social services disabled childrens team). You are entitled to a social care assessment for yourself as a carer and your child - that does not mean you are entitled to services, but you are entitled to a proper assessment (although not everyone wants social services involved and some have negative experiences, but our SW is great). Some hospitals have a community or learning disability nurse who can help with home issues eg safety, self care etc
My DS (now 5) is learning to be more social. He does not just pick it up, but it can be taught. Sadly I have yet to come across a mainstream school that has any proper training in how to teach social skills for asd, which is not surprising as its not part of teacher training, but you may get told that a weekly social skills group is all that is needed (as usually that is all they know how to do). Its not. You need to work on social skills every day.
DS does ABA (applied behaviour analysis) and they are great at teaching him to be more social and work with him at home and in school and support him in peer groups, playdates etc. Like you I didn't believe being social could be taught, just thought it was how DS was and we would have to accept it, but it can. It just has to be broken down and done in a really fun, systematic and rewarding way. I can see he is changing and much happier too. He is much more social with us, a very different child. The children at school are great with him, it helps that they understand he is different (he has speech delay) and that he struggles socially and they go out of their way to look after him. To his brothers disgust he can often be seen in the playground with two girls holding his hands dragging him along to join in. I wouldn't say he enjoys it yet, but he tolerates them and is beginning to initiate interactions with other children having blanked them up to now. We try and pair his favourite activities with other children so he builds positive associations between the two. I know that becoming more social is going to make him happier long term but it will take time and lots of work, its not going to just happen.
Diagnosis does not necessarily bring great swathes of help. You may find it just brings lots of professionals with very limited time and resources of dubious quality and effectiveness. Thats not to say don't go for a diagnosis, but its not a magic key to help. If you don't get good quality asd outreach straight off and can possibly afford it (and claim DLA, charity funds etc if necessary) try and find a good ABA supervisor or private ASD specialist speech therapist to help with social skills or read up on it yourself / look for courses. Then you can start putting in strategies now, even if its just at home / having children over to play after school in a more structured, focussed way.
There is a lot you can do to change the outcome. But the earlier the better, not least because at age 5 all the other kids are happy to play with DS and help him / make allowances and their play (boys in particular) is not very sophisticated but I am guessing that isn't going to last into juniors so you want to take advantage of the age of the other children and play based curriculum while you can.
Its tough finding the right help, but once you do you will feel much better as you will see things improving. My DS is quite severe ASD, but bright. With the right specialist help he is doing great and I feel really positive about his future. Our challenge for this year is to hold onto the support as the LA want to cut it to save money and put the once a week non specialist input back in!
You will find great support and advice here. Its been a total lifesaver for me at times.