Although multicollinearity gets a lot of attention, it is seldom the biggest problem facing studies like yours. My sense it that a lot of the attention to multicollinearity comes from data sets with tens to hundreds to thousands of predictors. That's not your situation.
What's most important is first to set up the model in a way that is best able to answer your question, without overfitting, in ways that deal with multicollinearity. A few thoughts on how you might proceed:
First, you seem to have a total score for the response variable that could reasonably be considered continuous (values from 1 to 96). Try modeling the response as a continuous variable instead of with binary or ordinal cutoffs. You would probably have to do some transformation of the scores (and perhaps of the confounders, too) to meet the requirements of a linear regression model, but I suspect that approach would give you a much better way to evaluate the +/- RDS differences. You could then present results as the coefficient (estimate and standard error) for +/- RDS in the regression model, with the confounders accounted for directly in the regression. That doesn't, however, deal with potential multicollinearity.
Second, you could use your understanding of the clinical issues to choose which of multiple correlated confounders to incorporate into the regression. With a continuous outcome in a standard linear regression model you can reasonably consider 1 predictor per 10 or so cases without overfitting, so you might be able to include RDS along with 4 or 5 thoughtfully chosen confounders and avoid multicollinearity issues that way.
Third, you could use methods that are designed to deal with multicollinearity. Penalized methods like ridge regression could even be considered to take advantage of multicollinearity by including all the variables into the model while lowering the magnitudes of their regression coefficients to prevent overfitting. In your situation you might consider leaving the RDS coefficient as unpenalized while penalizing the coefficients of the confounders.
Fourth, you could try using propensity scores to correct for the confounders. Although propensity scores are typically considered in the context of comparing treatment effects, they might provide a way to correct for the confounders in this +/- RDS context, for example with inverse probability weighting. One approach would use logistic regression to model the probability of having RDS as a function of the confounders, then to weight each case inversely proportional to its estimated probability of RDS given the values of its confounders.
For any of these approaches, however, I would recommend getting some local informed statistical help and using this as an opportunity to extend your knowledge about statistical analysis of clinical data.
