You can either run a repeated measures factorial anova (group x time); 4 levels of group as your between subjects factor and 3 levels of testing time as your within subjects factor. How you compare groups if you find a significant interaction depends on if you planned specific comparisons (i.e, you have a reason/theory predicting certain groups will differ) or if you want to explore the relationships between all possible comparisons.
Usually, if you have planned comparisons in mind, you can run multiple t-tests (controlling for an inflated type 1 error via bonferroni or holm procedures). If you don't know what to expect with your data, you can use a post hoc test (i.e, Tukey procedure) as an exploratory tool to see out of all the possible group comparisons, which are different. If you're using SPSS, theres also another kind of follow up procedure which I think might be more suitable; trend analysis. This tests linear, quadratic, etc relationships of your data - which I think is appropriate given your description of the data. Have a look into it.
With the repeated measures factorial anova approach, you may have problems regarding sphericity. Machauly's Test of Sphericity in SPSS will tell you if you have met this assumption. If you haven't you can go with one of the already laid out corrections in the SPSS Output (i.e, Greenhouse-Gieser for non sphericity).
If you find you can't meet the sphericity assumption even after correcting for non-sphericity, you might want to use a 1 way MANOVA - the MANOVA does not require sphericity. Here you would have one independent variable (group; 4 levels) and all the blood tests would serve as dependent variables (so you would have multiple DV's). You can do follow up comparisons for a MANOVA like how I stated above.
BTW, I'm a psych student as well. I read about a very similar study in my Psychopathology class. Very interesting stuff!
Best of Luck!