Is sagging and lumps normal during arm lipo recovery?

You mentioned you had two issues with your liposuction: lumpiness at 3 months' time and sagging skin on one arm. Presumably there is an asymmetry since one side is sagging and the other not.
The best course is generally to wait for about 6 months before considering revision liposuction, if any is needed at all. Lumpiness after liposuction generally responds to massage and time. Small irregularities generally respond to revision liposuction, if they are bothersome to the patient.
At the 6 month timepoint, it would also be good to assess the degree of skin looseness, especially if it is present on one side and not the other.
If the mass does not diminish in size over time, you should have your doctor consider the possibility that the mass might be something other than a post-liposuction indurated area. I have seen several cases where a patient has had liposuction, and a mass was then noted which was actually a separate growth rather than a post-liposuction irregularity. Fortunately these masses tend to be lipomas, but should generally be treated with surgical removal and biopsy rather than liposuction.

Thank you for your question.  Arms can be a very difficult area in which to get a great liposuction result.  At 3 months, you should be nearing the conclusion of your recovery.  Massage is unlikely to correct the irregularities at this point; and skin laxity will also be unlikely to reverse.  I would recommend waiting a few more months, at which point it may be reasonable to consider consultation for a limited brachioplasty (with or without additional lipo) to correct the problem.

It’s not unusual for patients to
have lumps, bumps, contour irregularities, and skin sag following upper arm
liposuction. Contour irregularities may have a variety of potential causes.
These may include differential swelling, fat necrosis, hematomas, and seromas.
They are usually transient and respond to conservative management with
compression garments and massage. Rarely, aspiration is necessary when
hematomas and seromas are present. In most cases, these problems have no effect
on the long term results of liposuction.

In other cases, loose upper arm
skin may result in the development of upper arm skin sag. When this occurs,
compression garments and conservative management may be successful, but
occasionally an upper arm brachioplasty may be necessary.

Since swelling can persist for 3
to 6 months following the procedure, secondary surgery should not be performed
for at least 6 months. It’s virtually impossible to make a recommendation
without a physical examination, especially since it’s only been 3 months since
surgery.

It’s important to stay in touch
with your plastic surgeon. Although, you’re not totally happy with your result,
this may change with time. If secondary surgery is indicated, your surgeon
should be able to formulate an appropriate treatment plan that addresses your
concerns. 

However you probably will not have that much more retraction of the skin at this stage.  You may need to have a mini-brachioplasty to correction the loose skin.  Hopefully you are enjoying and benefitting from the results of the surgery when wearing tight sleeved tops and sweaters.  I would suggest waiting at least a year before contemplating any other procedure.

It can take up to 6 months to see the final results of skin tightening after liposuction. What may help your post-op progress is a compression garment which will help keep the edema down and aid in skin retraction, though at three months the utility of the garment is minimal.
The lump itself may represent a hematoma or unaspirated fat depending on the liposuction technique. Continue massage and reassess at six months.
Of course you should discuss your post-operative progress with your treating surgeon.
Good luck!

Hopefully, you will have some more retraction of the skin and evening out of the lumpy areas. Give it a little more time. It can take six months to a year for full healing.