Sensitive watery eyes, recommendations please

You might have blepharitis, eye makeup is probably not a good idea . I havnt worn any for months due to the same problem.

I also have Blepharitis and never wear eye makeup. There is a lotion you can get for this condition, also eye drops, which I have on prescription.

I use wipes, I think they're called Blephaclean or something.

I've been prescribed eye drops and a cream for watery eyes. The doctor scared me because he could see some damage on my cornea from the excessive dryness which could lead to serious visual impairment. It might be a good idea to get your eyes checked to see if there's an issue first.

I do have blepharitis, but I treat it carefully and it hasn't been a problem for a long while

I have dry sensitive eyes and prescribed Tear Lac serum which stays in the eye instead of drops which run down back of throat

It is possible that you have a blocked tear duct. This causes constantly running eyes which causes soreness.
I needed surgery to repair my blocked tear duct.
I also have dry eyes and surprising as it may seem, that too can cause watery eyes. I needed steroid drops over a period of nine months as I had ulcers at the back of my eyes before the condition was diagnosed.
This was years ago and the treatment was successful. I still have drops for dry eyes, on prescription from my consultant.

PS....in answer to your question regarding eye makeup.... AVOID.
I wouldn't put anything on my eye lids.

Gave up wearing eye makeup years ago as everything caused an irritation

I prefer gel to eye drops I have multiple eye problems, I'm now partially visually impaired.

Before self treating, please get your eyes checked.