Is this Phimosis ?

Is foreskin not moving down itself when erect Phimosis? I can move it down manually myself, and it feels ever so slightly tight.

It is Phimosis but it’s mild/moderate version, nothing to be too worried about just yet. Although, it would be beneficial if you worked on the treatment straight away.
There are certain Phimosis stretching exercises (aka foreskin stretching exercises) that you can do. There’s also Phimosis rings that you can buy.
I’d advise you to google “Phimosis stretching exercises” and “Phimosis ring” and do some digging around on those topics and find what’s best for you. Just make sure that when you do stretching exercises, you take it easy and not stretch it too hard too fast as it can lead to painful tears. Avoid prone masturbation (Prone masturbation is: lie face-down on your chest and masturbate. You may thrust your penis against a mattress, pillow, or the floor. You may also cup your penis and testicles and thrust into your hands)
Speak to your GP/doctor and get referred to a urologist if you see no progress after a few weeks.

My suggestion would be to practice stretching exercises by starting easy, as you would with any new, or gym exercise then build on these over a period of months, rather than days or weeks.
Yes, stretching can work for some men within a matter of days or even weeks, where other take months to achieve noticeable differences.
The best exercises I know of are at:

  • Wiki - How - 3 Ways to do - Phimosis Stretching