It is hard being a mom to a toddler. It sounds to me like you are feeling super stressed, so step back and recognize that. Try to take a little time to meditate, or pray or stretch or whatever energizes you (I know its hard to find time for these things, but just 5 minutes while he eats or naps can help) My next suggestion is to remember that your recent move has also been stressful for your toddler. We moved just a couple months ago, and my dd has had a very hard time adjusting. She went through a phase of not being willing to leave the house for about a month, and then it passed. Some of your son's screaming may be a reaction to the move, missing old friends, feeling lost, etc.
I bet you can call the local hospital to get the number of the LLL to contact them about the next meeting.
As for the communication- can you make a picture board with basic items on it that your ds can point to to communicate with you? A glass to ask for a drink, a picture of some simple food items, a diaper, etc. you explain to him he then shows you what he wants with the picture. Or you can work harder with the signs, if you learn them and use them all the time, he'll pick them up. My dd is very vocal, so I haven't had to try these, but I do know that she still doesn't use words like "hungry" and she speaks in sentences. Expressing how they feel is hard for toddlers. Try to remember he's still a baby, even though he's turning into a child.
I wish you well, it is hard setteling into a new place, heaven knows I'm still struggeling with it.