Mn is full of extremely lonely women of all ages, so if you want reassurance that you're not alone, you will find it in spades.
However, no, I wouldn't say it was 'normal' in the sense that everyone, or almost everyone, is lonely in their thirties, or, as you say you do, has always struggled to make/keep friendships.
In my 30s, (I was with my longtime DP, but didn't have my son until I was almost 40, and was working FT in a demanding job a long distance from home, which meant I commuted weekly), my friendships were mostly with old student friends, colleagues from current and previous jobs, some random people I'd met through other people, or out doing stuff.
The only time I've struggled with friendships and loneliness was during a disastrous period of some years living in a village after we moved out of London while I was on maternity leave. Looking back, it was an insular place and my face didn't fit. Pretty much everyone else had always lived there, and the other parents at baby/toddler groups and later on the school run had all gone to school together and had always known one another, and just weren't used to the idea that you might make friends with someone from somewhere else, who was different to you. To whom you might need to introduce yourself and ask questions you didn't know the answers to.
If you want friends, you will have to go out and make them.