Need help fast spider mites on flowering plant

I have been battling with the aphids for some time now. Every 2 days or so i would clean the leafs of the plant with soapy water, but now the problem is that the flowers are beginning to produce resin and i dont want to wash that off.
4 days without any cleaning and the plant is full of mites some of the leafs are already yellow. I stripped away the worst infected leafs and squished with my finger as many mites i could on the remaining leafs.
I heard that neem oil gives a bad taste if it gets in the flowers .
I really don't know what to do.
I'm about 3 weeks into flowering stage. can someone tell me an approximation of the time i am supposed to harvest. i know that the resin should become milky.
Its my first grow. Last plant standing. It will be my first smoke ever, i don't want to mess this up after all this waiting.

I`ve used neem oil right up till 3 weeks before cutting them down,,,my hydroshop guy told me he`s used it before but never go beyond that,,,also give it a real good rinse before you tear it down,,

I have had great success using Isopropyl alcohol and water.. mix 50/50 with 99%iso and water, then mist your leaves top and bottom right when your lights come on. Try not to soak the plant as you dont want to wash off all that sticky resin ;) Do this every 2-3 days untill 2 weeks before havest (usually week 6 or 7 depending if you have an 8 or 9 week strain) Alcohol is a poison and will kill the mites on contact, and it dries very quickly compared to water.. so there is very small chance of it causing bud mold. You want to spray as close to lights on as possible so that the solution dries up quickly. A few hours after you spray with the alcohol, (or once the plants are nice and dry again) you can try a light mist of seaweed extract like Growth Plus as a foilar spray. Seaweed has natural anti-fungal properties and will help strengthen your plants resistence to molds and mildew.. I use it every day when my lights come on as a foilar feed.. the stuff works excellent! Mites are super hard to battle through the bud stage, I usually try to get rid of them before I transfer the plants to my flower room to avoid having to spray while flowering. You may not be able to completely get rid of them, but the spray should at least keep them at bay and save your crop for the most part. At worst the alcohol will get you drunk when you smoke your buds.. LOL... Good luck!

I have also heard that ladybugs work very well for controlling insects.. especially aphids.. but they will eat mites too!