Will my surgery area drain itself after the draining tube was removed?

Thank you for sharing your question and I am sorry to hear of your recovery difficulties.  Though impossible to offer definite advice without an in-person examination it sounds as if you have developed an infection at your operative site.  I would recommend contacting your surgeon's office immediately.  This fluid will need to be drained while antibiotics administered to clear the infection.  Offices should have a surgeon on-call to be able to assist you.  Hope this helps.

Surgical judgement and experience dictates the timing of drain removal. When a certain volume is reached, they can be removed safely with the thought that small amounts of fluid will subsequently be absorbed by surrounding tissue.Apply Scar Serum to reduce scarring and avoid sun exposure to prevent hyperpigmentation of the wound. 
H Karamanoukian MD FACS

Sometimes, after removal of the drain following lipoma removal, fluid reaccumulates. This can resorb on its own if it is a small amount. If ther is alot of fluid aspiration with a needle in the office and rarely, replacement of the drain may be required. The fact that your surgical site is red and painful suggests you may have an infection. Please consult your surgeon immediately for evaluation. You may need aspiration of the fluid and antibiotic therapy. Good luck and take care.

Fluid build up in a surgery site is normal- it comes from the tissue surfaces leaking fluid to cushion and clean themselves as they heal. We call this a seroma. Once the tissue has a chance to heal and seal itself back together, the fluid decreases and the body eventually resorbs what it made. If there's a lot of fluid at the surgical site and not a lot of coverage between the fluid in the incision, sometimes the fluid can make its way out of the incision and leak through the skin. This isn't dangerous, but it can be messy. Ideally, we like to wick away the fluid with a drain to allow healing tissue surfaces more opportunity to be in contact with one another and stick together. If the drain was removed before the tissue site was dry enough, sometimes fluid can re-accumulate in the surgery site. This is usually easily solved by draining the fluid with a needle or placing another drain with ultrasound guidance. Sometimes if the amount of fluid a small enough, simple watching and waiting will allow the body to absorb it and eventually it will go away. If the area is incredibly painful, swollen, and very red, or if you have flu like symptoms or fever, there can be infection at the site. This should be evaluated by your doctor soon as possible.