I would suggest to first take the individual differences. That way you would eliminate the the individual factor and the individual would act as her own control. Just as usual in a paired t-test.

If the data are recorded like in variables like "strength_left" and "strength_right", then I would take the difference (and create the variable "ind_dif"):

ind_dif = strength_left - strength_right

If there is no difference between affected and not affected side, then you would expect numbers around zero, both positive and negative values.

(I guess here that the non-affected side is stronger than the other side on the average)

if the right side is the affected one, then you would expect positive numbers like:

ind_dif = strength_left - strength_right

10 = 21 - 11

if the left side is the affected one, then you would expect negative numbers like:

ind_dif = strength_left - strength_right

-11 = 12 - 23

So then you need to change the sign on "ind_dif" by multiplying by minus one ( -1).

That can be done by transforming the "affected" variable which so far takes values (0=right and 1= left).

affected_new =2*(affected - 0.5)

The affected_new will take value = +1 for left side and -1 for right side.

Now you need to multiply "ind_dif" by affected_new to:

well_vs_affected = ind_dif*affected_new

If you get many positive values, that is the mean on "well_vs_affected" is positive, then there is indication that the "well side" is stronger than the affected side.

But you also had two treatments. Then you can run the variable "well_vs_affected" with a two sample independent t-test. (An equivalent result will be given if you run an one way analysis of variance (anova) with "well_vs_affected" as dependent variable and treatment as an explanatory/independent variable.)