I can understand your concerns about lymphedema exacerbation with pregnancy.

Weight, hormonal and fluid changes that typically occur with pregnancy vary from woman to woman as well as from pregnancy to pregnancy within the same woman. Mechanical compression from pregnancy has been attributed to new onset lymphedema. The physiologic changes in pregnancy have the potential to increase your swelling from lymphedema, at least in the short run until after you deliver and return to your preconception baseline.

 Review of the literature revealed few studies looking at "worsening" of lymphedema from pregnancy.  While attempting to answer a legitimate concern, the studies were retrospective, lacked objective before and after measurements, had a small number of participants, failed to describe lymphedema treatment practices by the study participants and did not document efficacy of treatment.  Study results did not agree in terms of long term consequences.

 Worldwide, pregnancy in women with lymphedema is not an unheard of event  considering the number of women of child bearing age with lymphedema for reasons beyond mastectomies - congenital or inherited syndromes, infections, trauma to name a few

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Discussing your concerns with your breast surgeon, ob-gyn and lymphedema therapist will give you more information to make an informed decision.   Perhaps someone within your local lymphedema support group or network has managed their lymphedema throughout a pregnancy and can share helpful management advice.

If you do decide to become pregnant, your lymphedema therapist can help monitor any size change; making adjustments in treatment regimens, garment sizes, wrapping, etc. to assure continued adequacy of therapy  in addition to being an excellent source of emotional support.  

You also asked about information on strengthening your affected arm.  You must have some weakness in your affected arm or you would not be asking about recommendations.  Here I suggest you consult a physical therapist who is well versed in assessing and developing strengthening programs for post mastectomy extremities.

 In the past, exercise and lymphedema were not mentioned in the same sentence.  In fact exercise was shunned and almost forbidden. We now know exercise and maintenance of muscle integrity is good.  Exercise recommendations for someone with versus without lymphedema vary. The ways they vary include: pace, intensity, type of exercise, exercise environment (temperature, risk of trauma), and protective equipment. Body area with lymphedema and personal level of physical conditioning add extra dimensions to exercise recommendations.  Monitoring of lymphedema with activity is vital.  Adjustments of self care management to maintain a good level of lymphedema control may become necessary. With trial and error one learns what is possible and how to achieve more without loss of control in lymphedema management.