I've been trying to masturbate for a while, but never orgasmed or squirted. I do get the need to pee and things like that while I'm masturbating, and I can feel it coming until my vagina starts pulsing and I squirm around uncontrollably. I think you feel that when you orgasm, but I don't feel anything really significant. I'm also 13.
What you described is an orgasm by any definition I have encountered. Not all orgasms are equal, sometimes they are weak and other times strong. Have you ever continued past the uncontrollable squirming stage? Many women are capable of more than one orgasm. Sometimes the 1st isn't that good, but the next one better, and at some point mind blowing.
Are engaging in enough foreplay? I know that sounds odd but it is actually still important during solo sex. Drawing it out, massaging yourself - breasts and other sensitive areas, teasing yourself essentially, can greatly increase your stimulation.
Do you fantasize before and during masturbation? Your mind is your biggest sex organ.
Have you explored massaging your g-spot and other areas in your vagina that are sensitive after full arousal? Search online for the g-spot, urethral sponge, female prostrate (yes, there is one), clitoris including the clitoral "legs".
What are your expectations about orgasms? Could this be affecting your experience?
An orgasm does not necessarily lead to squirting. Many women have never squirted despite many years of having sex. (The liquid produced is normally directed elsewhere in the body. Was it the bladder?) Although it is something that can be learned. For the real deal on squirting research the female prostate, as mentioned above.
Many women have better orgasms as they get older, especially with practice, so I expect they will get better. That is something you can look forward to in any case.